ODSC West 2021: Network Analysis
Clinton Brownley
11/17/2021
Install packages
Install igraph and some additional packages to process and plot the network data.
# ,echo=FALSE, include=FALSE
# install.packages("statnet")
if (!require("pacman")) install.packages("pacman")
pacman::p_load("ape",
"d3r",
"ergm",
"ggplot2",
"jsonlite",
"tidyverse",
"igraph",
"lubridate",
"purrr",
"RColorBrewer",
"sand",
"sqldf",
"wrapr")Load packages
Load igraph and some additional packages to process and plot the network data.
# ,echo=FALSE, include=FALSE
library("ape")
library("d3r")
library("ergm")
library("ggplot2")
library("jsonlite")
library("dplyr")
library("igraph")
library("lubridate")
library("purrr")
library("RColorBrewer")
library("readr")
library("sand")
library("sqldf")
library("wrapr")Network Analysis
Lord of the Rings
Read Data
Ontology
Read CSV data from the morethanbooks Lord of the Rings Networks repository into a tibble.
ontology.csv contains the basic metadata about each entity (i.e. proper names used to reference characters, places, or groups) together with its identifier (e.g. the identifier for Aragorn is “arag”).
ontology = tibble(read.csv(url("https://raw.githubusercontent.com/morethanbooks/projects/master/LotR/ontologies/ontology.csv"), sep = "\t"))
names(ontology) <- c("id", "type", "label", "freqsum", "subtype", "gender")
head(ontology)## # A tibble: 6 × 6
## id type label freqsum subtype gender
## <chr> <chr> <chr> <int> <chr> <chr>
## 1 andu pla Anduin 109 pla ""
## 2 arag per Aragorn 1069 men "male"
## 3 arat per Arathorn 36 men "male"
## 4 arwe per Arwen 51 elves "female"
## 5 bage pla Bag End 77 pla ""
## 6 bali per Balin 30 dwarf "male"Books 1, 2, 3 Combined
Read CSV data from the morethanbooks Lord of the Rings Networks repository into a tibble.
networks-id-3books.csv contains an edges table with the number of times two entities are mentioned in the same paragraph across all three books of the series.
In this project, the nodes represent entities (i.e. proper names used to reference characters, places, or groups), and two of them are connected by an edge if in any paragraph there are references to these two entities.
Across the three books, Frodo and Sam are referenced in the same paragraph most frequently (533 paragraphs), and Frodo and Gandalf are referenced in the second most number of paragraphs(181 paragraphs).
books123 = tibble(read.csv(url("https://raw.githubusercontent.com/morethanbooks/projects/master/LotR/tables/networks-id-3books.csv"), sep = ","))
books123 <- books123 %>%
dplyr::select("IdSource", "IdTarget", "Weight", "Type") %>%
dplyr::mutate("Type" = "Books 123",
"Weight" = as.double(Weight))
names(books123) <- c("source", "target", "weight", "volume")
head(books123)## # A tibble: 6 × 4
## source target weight volume
## <chr> <chr> <dbl> <chr>
## 1 frod sams 533 Books 123
## 2 frod ganda 181 Books 123
## 3 merr pipp 162 Books 123
## 4 arag frod 146 Books 123
## 5 frod goll 127 Books 123
## 6 bilb frod 126 Books 123Book 1
Read CSV data from the morethanbooks Lord of the Rings Networks repository into a tibble.
networks-id-volume1.csv contains an edges table with the number of times two entities are mentioned in the same paragraph in The Fellowship of the Ring, published on July 29, 1954.
book1 = tibble(read.csv(url("https://raw.githubusercontent.com/morethanbooks/projects/master/LotR/tables/networks-id-volume1.csv"), sep = ","))
book1 <- book1 %>%
dplyr::select("IdSource", "IdTarget", "Weight", "Type") %>%
dplyr::mutate("Type" = "Book 1",
"Weight" = as.double(Weight))
names(book1) <- c("source", "target", "weight", "volume")
book1 <- book1 %>% mutate("title" = "The Fellowship of the Ring",
"publication_date" = lubridate::ymd("1954-07-29"))
head(book1)## # A tibble: 6 × 6
## source target weight volume title publication_date
## <chr> <chr> <dbl> <chr> <chr> <date>
## 1 frod sams 171 Book 1 The Fellowship of the Ring 1954-07-29
## 2 frod ganda 129 Book 1 The Fellowship of the Ring 1954-07-29
## 3 arag frod 105 Book 1 The Fellowship of the Ring 1954-07-29
## 4 bilb frod 96 Book 1 The Fellowship of the Ring 1954-07-29
## 5 frod pipp 80 Book 1 The Fellowship of the Ring 1954-07-29
## 6 pipp sams 72 Book 1 The Fellowship of the Ring 1954-07-29Book 2
Read CSV data from the morethanbooks Lord of the Rings Networks repository into a tibble.
networks-id-volume2.csv contains an edges table with the number of times two entities are mentioned in the same paragraph in The Two Towers, published on November 11, 1954.
book2 = tibble(read.csv(url("https://raw.githubusercontent.com/morethanbooks/projects/master/LotR/tables/networks-id-volume2.csv"), sep = ","))
book2 <- book2 %>%
dplyr::select("IdSource", "IdTarget", "Weight", "Type") %>%
dplyr::mutate("Type" = "Book 2",
"Weight" = as.double(Weight))
names(book2) <- c("source", "target", "weight", "volume")
book2 <- book2 %>% mutate("title" = "The Two Towers",
"publication_date" = lubridate::ymd("1954-11-11"))
head(book2)## # A tibble: 6 × 6
## source target weight volume title publication_date
## <chr> <chr> <dbl> <chr> <chr> <date>
## 1 frod sams 158 Book 2 The Two Towers 1954-11-11
## 2 goll sams 101 Book 2 The Two Towers 1954-11-11
## 3 frod goll 99 Book 2 The Two Towers 1954-11-11
## 4 merr pipp 51 Book 2 The Two Towers 1954-11-11
## 5 gimli lego 50 Book 2 The Two Towers 1954-11-11
## 6 ganda saru 49 Book 2 The Two Towers 1954-11-11Book 3
Read CSV data from the morethanbooks Lord of the Rings Networks repository into a tibble.
networks-id-volume3.csv contains an edges table with the number of times two entities are mentioned in the same paragraph in The Return of the King, published on October 20, 1955.
book3 = tibble(read.csv(url("https://raw.githubusercontent.com/morethanbooks/projects/master/LotR/tables/networks-id-volume3.csv"), sep = ","))
book3 <- book3 %>%
dplyr::select("Source", "Target", "Weight", "Type") %>%
dplyr::mutate("Type" = "Book 3",
"Weight" = as.double(Weight))
names(book3) <- c("source", "target", "weight", "volume")
book3 <- book3 %>% mutate("title" = "The Return of the King",
"publication_date" = lubridate::ymd("1955-10-20"))
head(book3)## # A tibble: 6 × 6
## source target weight volume title publication_date
## <chr> <chr> <dbl> <chr> <chr> <date>
## 1 frod sams 193 Book 3 The Return of the King 1955-10-20
## 2 ganda pipp 79 Book 3 The Return of the King 1955-10-20
## 3 merr pipp 45 Book 3 The Return of the King 1955-10-20
## 4 arag ganda 34 Book 3 The Return of the King 1955-10-20
## 5 dene ganda 34 Book 3 The Return of the King 1955-10-20
## 6 dene pipp 34 Book 3 The Return of the King 1955-10-20Create a DataFrame from the books123 edgelist for an undirected graph
We can use sqldf to create a R data frame that combines the edges data from books123 and the metadata about the entities from ontology. The result is a data frame with all of the information we have about the paragraph references to pairs of entities across all three books.
We have undirected data, i.e. a particular person can appear as the source or the target and we’re not interested in the distinction (direction), so we can make it easier to get the ego network (the network that is “visible” to a certain person) by duplicating each row with its inverse. This way, we can group by a single column to get the ego network.
For simplicity in this early cell, and because this processing isn’t actually needed for igraph, we don’t perform this processing in this cell; however, we do perform it in the next cell to illustrate the difference between these methods.
Note that in the data frame row filtering shown in this cell we have to search for Frodo both as a source or as a target to select all of the rows (edges) associated with Frodo’s ego network. In the next cell, we will see that conducting the processing in the SQL query will make it easier for us to identify character ego networks.
g_df <- sqldf::sqldf("
SELECT
sour.id AS source_id, sour.label as source_name, sour.type AS source_type, sour.subtype AS source_subtype, sour.gender AS source_gender,
dest.id AS target_id, dest.label AS target_name, dest.type AS target_type, dest.subtype AS target_subtype, dest.gender AS target_gender,
conn.weight, conn.volume
FROM
books123 conn
JOIN ontology sour
ON
conn.source = sour.id
JOIN ontology dest
ON
conn.target = dest.id"
)
g_df %>%
dplyr::filter(source_name == "Frodo" | target_name == "Frodo", source_type == "per", target_type == "per") %>%
dplyr::arrange(source_id, desc(weight)) %>%
head(10)## source_id source_name source_type source_subtype source_gender target_id
## 1 arag Aragorn per men male frod
## 2 arat Arathorn per men male frod
## 3 arwe Arwen per elves female frod
## 4 bali Balin per dwarf male frod
## 5 bere Beregond per men male frod
## 6 bilb Bilbo per hobbit male frod
## 7 bill Bill per animal male frod
## 8 boro Boromir per men male frod
## 9 cele Celeborn per elves male frod
## 10 dene Denethor per men male frod
## target_name target_type target_subtype target_gender weight volume
## 1 Frodo per hobbit male 146 Books 123
## 2 Frodo per hobbit male 2 Books 123
## 3 Frodo per hobbit male 6 Books 123
## 4 Frodo per hobbit male 4 Books 123
## 5 Frodo per hobbit male 1 Books 123
## 6 Frodo per hobbit male 126 Books 123
## 7 Frodo per hobbit male 9 Books 123
## 8 Frodo per hobbit male 68 Books 123
## 9 Frodo per hobbit male 1 Books 123
## 10 Frodo per hobbit male 7 Books 123# Number of references (edges) between Frodo and other people across the three books: 38
g_df %>%
dplyr::filter(source_name == "Frodo" | target_name == "Frodo", source_type == "per", target_type == "per") %>%
dim()## [1] 38 12Create a DataFrame with bidirectional edgelists for an undirected graph
We have undirected data, so to make it easier to work with we’re going to duplicate each row with its inverse. This way, we can group by a single column to get the ego network (the network that is “visible” to a certain person).
In contrast to the previous cell, we perform this processing step in the SQL query here to illustrate the difference between these methods.
Note that in the data frame row filtering shown in this cell we have to search for Frodo only in the source column to select all of the rows (edges) associated with Frodo’s ego network.
Again, this processing isn’t actually needed for igraph, we’re doing it for manual manipulation of the graph.
network_df <- sqldf::sqldf("
SELECT
sour.id AS source_id, sour.label as source_name, sour.type AS source_type, sour.subtype AS source_subtype, sour.gender AS source_gender,
dest.id AS target_id, dest.label AS target_name, dest.type AS target_type, dest.subtype AS target_subtype, dest.gender AS target_gender,
conn.weight, conn.volume
FROM
books123 conn
JOIN ontology sour
ON
conn.source = sour.id
JOIN ontology dest
ON
conn.target = dest.id
UNION
SELECT
dest.id AS source_id, dest.label as source_name, dest.type AS source_type, dest.subtype AS source_subtype, dest.gender AS source_gender,
sour.id AS target_id, sour.label AS target_name, sour.type AS target_type, sour.subtype AS target_subtype, sour.gender AS target_gender,
conn.weight, conn.volume
FROM
books123 conn
JOIN ontology sour
ON
conn.source = sour.id
JOIN ontology dest
ON
conn.target = dest.id"
)
network_df %>%
dplyr::filter(source_name == "Frodo", source_type == "per", target_type == "per") %>%
dplyr::arrange(source_id, desc(weight)) %>%
head(10)## source_id source_name source_type source_subtype source_gender target_id
## 1 frod Frodo per hobbit male sams
## 2 frod Frodo per hobbit male ganda
## 3 frod Frodo per hobbit male arag
## 4 frod Frodo per hobbit male goll
## 5 frod Frodo per hobbit male bilb
## 6 frod Frodo per hobbit male pipp
## 7 frod Frodo per hobbit male merr
## 8 frod Frodo per hobbit male boro
## 9 frod Frodo per hobbit male fara
## 10 frod Frodo per hobbit male elro
## target_name target_type target_subtype target_gender weight volume
## 1 Sam per hobbit male 533 Books 123
## 2 Gandalf per ainur male 181 Books 123
## 3 Aragorn per men male 146 Books 123
## 4 Gollum per hobbit male 127 Books 123
## 5 Bilbo per hobbit male 126 Books 123
## 6 Pippin per hobbit male 115 Books 123
## 7 Merry per hobbit male 86 Books 123
## 8 Boromir per men male 68 Books 123
## 9 Faramir per men male 55 Books 123
## 10 Elrond per elves male 39 Books 123# Number of references (edges) between Frodo and other people across the three books: 38
network_df %>%
dplyr::filter(source_name == "Frodo", source_type == "per", target_type == "per") %>%
dim()## [1] 38 12Filter for pairs of entities that were mentioned in the same paragraph at least twice and then sort by weight and source_id
# Filter for edges with weights >= 2
network_df %>%
dplyr::filter(weight >= 2) %>%
dplyr::arrange(weight, source_id) %>%
head(10)## source_id source_name source_type source_subtype source_gender target_id
## 1 andu Anduin pla pla dwar
## 2 andu Anduin pla pla elro
## 3 andu Anduin pla pla fara
## 4 andu Anduin pla pla goll
## 5 andu Anduin pla pla orth
## 6 arag Aragorn per men male osgi
## 7 arat Arathorn per men male arwe
## 8 arat Arathorn per men male frod
## 9 arat Arathorn per men male gimli
## 10 arat Arathorn per men male mord
## target_name target_type target_subtype target_gender weight volume
## 1 Dwarves gro dwarf 2 Books 123
## 2 Elrond per elves male 2 Books 123
## 3 Faramir per men male 2 Books 123
## 4 Gollum per hobbit male 2 Books 123
## 5 Orthanc pla pla 2 Books 123
## 6 Osgiliath pla pla 2 Books 123
## 7 Arwen per elves female 2 Books 123
## 8 Frodo per hobbit male 2 Books 123
## 9 Gimli per dwarf male 2 Books 123
## 10 Mordor pla pla 2 Books 123Check that the same number of source and target nodes were created
c( length(unique(network_df$source_id)), length(unique(network_df$target_id)) )## [1] 73 73Count the number of nodes that are: group, person, place, thing
Here, we are interested in the people, so when we create our network graph we will only include the per nodes and edges, i.e. the ones associated with people.
network_df %>% group_by(source_type) %>% count()## # A tibble: 4 × 2
## # Groups: source_type [4]
## source_type n
## <chr> <int>
## 1 gro 317
## 2 per 1614
## 3 pla 896
## 4 thin 61Create a network graph of people with edge weights greater than 20
igraph has many functions for reading and writing graphs and converting to and from other data formats. We can create a network graph G from a R data frame using igraph’s graph_from_data_frame function.
A graph G = (V, E) is mathematical structure with a set V of elements, called vertices or nodes, and a set E of pairs of nodes, called edges or links. A network can be undirected or directed. In addition, a network can be unweighted or weighted.
To convert the edgelist data in the data frame into a graph G using graph_from_data_frame, the data frame must contain an edge list representation of a graph, i.e. two columns of node names and zero or more columns of edge attributes. Each row will be processed as one edge instance.
d is a data frame containing a symbolic edge list in the first two columns. Additional columns are considered as edge attributes. Since version 0.7 this argument is coerced to a data frame with as.data.frame..
directed is a logical scalar, whether or not to create a directed graph.
vertices is a data frame with vertex metadata, or NULL. Since version 0.7 this argument is coerced to a data frame with as.data.frame, if not NULL.
Given our interest in characters, we restrict the graph to references about people. In addition, we further restrict our attention to pairs of people who are referenced together more than 20 times across all the books to reduce the number of edges such that, for readability, the edge count is not more than four times the node count [Melancon 06].
my_edges <- sqldf::sqldf("
SELECT
sour.label as source_name, sour.type as source_type,
dest.label AS target_name, dest.type AS target_type,
conn.weight
FROM
books123 conn
JOIN ontology sour
ON
conn.source = sour.id
JOIN ontology dest
ON
conn.target = dest.id"
) %>%
dplyr::filter(source_type == "per", target_type == "per", weight > 20) %>%
dplyr::select(source_name, target_name, weight) %>%
dplyr::rename(from = source_name, to = target_name)
my_nodes <- network_df %>%
dplyr::filter(source_type == "per", target_type == "per", weight > 20) %>%
dplyr::select(source_name, source_type, source_subtype, source_gender, volume) %>%
dplyr::rename(name = source_name, type = source_type, subtype = source_subtype, gender = source_gender) %>%
dplyr::distinct()
G <- graph_from_data_frame(my_edges, directed = FALSE, vertices = my_nodes)
#print_all(G)
G## IGRAPH 670f9cf UNWB 31 79 --
## + attr: name (v/c), type (v/c), subtype (v/c), gender (v/c), volume
## | (v/c), weight (e/n)
## + edges from 670f9cf (vertex names):
## [1] Frodo --Sam Frodo --Gandalf Merry --Pippin Aragorn--Frodo
## [5] Frodo --Gollum Bilbo --Frodo Gandalf--Pippin Aragorn--Gandalf
## [9] Gollum --Sam Frodo --Pippin Gimli --Legolas Pippin --Sam
## [13] Frodo --Merry Aragorn--Legolas Aragorn--Sam Aragorn--Gimli
## [17] Gandalf--Saruman Boromir--Frodo Aragorn--Merry Aragorn--Pippin
## [21] Aragorn--Boromir Merry --Sam Aragorn--Elrond Gandalf--Théoden
## [25] Faramir--Frodo Bilbo --Gandalf Gandalf--Gimli Gandalf--Sam
## + ... omitted several edgesPlot the nodes of the LotR network
set.seed(10)
igraph_options(vertex.size=6,
vertex.color="blue",
vertex.frame.color="blue",
vertex.label=NA, # V(G)$name,
edge.color=NA)
par(mfrow=c(1,1))
plot(G, layout=layout_randomly) # layout_nicely
title("LotR network (no edges!)")
Plot the nodes and edges of the LotR network
e.size <- 4 * E(G)$weight / max( E(G)$weight, na.rm = TRUE )
set.seed(10)
igraph_options(vertex.size=6,
vertex.color="blue",
vertex.frame.color="blue",
vertex.label=NA, # V(G)$name,
edge.width=e.size,
edge.color="blue")
par(mfrow=c(1,1))
plot(G, layout=layout_randomly) # layout_nicely
title("LotR network")
Number of nodes
Sometimes the number of vertices (also called nodes) in a graph is called the order of the graph. We can get the number of nodes in a graph with gorder(G).
# Count the number of nodes
gorder(G)## [1] 31vcount(G)## [1] 31List of nodes
# List all of the nodes
V(G)## + 31/31 vertices, named, from 670f9cf:
## [1] Aragorn Arathorn Arwen Beregond Bilbo Bill Boromir
## [8] Celeborn Denethor Elendil Elrond Éomer Éowyn Faramir
## [15] Frodo Galadriel Gandalf Gimli Glóin Gollum Isildur
## [22] Legolas Merry Pippin Sam Saruman Sauron Shadowfax
## [29] Théoden Bombadil TreebeardList neighbors of a node
# List neighbors of node "Aragorn"
neighbors(G, "Aragorn")## + 17/31 vertices, named, from 670f9cf:
## [1] Arathorn Arwen Boromir Elendil Elrond Éomer Faramir Frodo
## [9] Gandalf Gimli Legolas Merry Pippin Sam Saruman Sauron
## [17] ThéodenDetermine the degree of each node in the graph
G_degree <- degree(G)
# Arrange nodes alphabetically
# G_degree[sort(names(G_degree))]
# Arrange nodes in descending order of degree
G_degree[order(G_degree, decreasing = TRUE)]## Gandalf Aragorn Frodo Pippin Sam Merry Boromir Faramir
## 18 17 14 11 10 9 7 7
## Gimli Legolas Saruman Treebeard Bilbo Denethor Elrond Éomer
## 7 6 5 5 4 4 4 4
## Sauron Théoden Gollum Arwen Elendil Éowyn Arathorn Beregond
## 4 4 3 2 2 2 1 1
## Bill Celeborn Galadriel Glóin Isildur Shadowfax Bombadil
## 1 1 1 1 1 1 1G_degree <- degree(G)
# Arrange nodes alphabetically
# G_degree[sort(names(G_degree))]
# Arrange nodes in descending order of degree
G_degree_distribution <- G_degree[order(G_degree, decreasing = TRUE)]
# Alternatively: tibble::enframe(G_degree_distribution) # returns columns `name` and `value`
G_degree_distribution <- data.frame(Character=factor(names(G_degree_distribution)),
Degree=G_degree_distribution,
row.names=NULL) %>% arrange(desc(Degree))
ggplot(data = G_degree_distribution, aes(x = reorder(Character, -Degree), y = Degree)) +
geom_col(aes(fill = Degree)) +
scale_color_distiller(palette = "Blues", direction = 1, aesthetics = c("colour", "fill")) +
scale_y_continuous(breaks=seq(0, 20, 2.5), limits = c(0, 20)) +
# ylim(0, 20) +
labs(title = "Degree Distribution of LotR Characters") +
xlab("Character") +
theme_light() +
theme(legend.position = "none",
panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
plot.title = element_text(hjust = 0.5),
axis.text.x = element_text(angle = 90))
Determine the average degree of the graph
The average degree of a network is
\[\begin{align} \langle k \rangle = \frac{\sum_{i=1} k_i}{N} \end{align}\]
round(mean(degree(G), na.rm = TRUE), 2)## [1] 5.1# The average degree of an undirected network equals 2L / N
round( 2 * length(E(G)) / length(V(G)), 2)## [1] 5.1Number of edges
Sometimes the number of edges (also called links) in a graph is called the size of the graph. We can get the number of edges in a graph with ecount(G).
# Count the number of edges
ecount(G)## [1] 79List of edges
# List all of the edges
E(G)## + 79/79 edges from 670f9cf (vertex names):
## [1] Frodo --Sam Frodo --Gandalf Merry --Pippin
## [4] Aragorn --Frodo Frodo --Gollum Bilbo --Frodo
## [7] Gandalf --Pippin Aragorn --Gandalf Gollum --Sam
## [10] Frodo --Pippin Gimli --Legolas Pippin --Sam
## [13] Frodo --Merry Aragorn --Legolas Aragorn --Sam
## [16] Aragorn --Gimli Gandalf --Saruman Boromir --Frodo
## [19] Aragorn --Merry Aragorn --Pippin Aragorn --Boromir
## [22] Merry --Sam Aragorn --Elrond Gandalf --Théoden
## [25] Faramir --Frodo Bilbo --Gandalf Gandalf --Gimli
## [28] Gandalf --Sam Aragorn --Éomer Gandalf --Legolas
## + ... omitted several edgesDetermine the density of the graph
The density of a network is the fraction of possible links that actually exist, which is the same as the fraction of pairs of nodes that are actually connected. The average degree of a network is related (directly proportional) to its density. The density is the ratio between the average and maximum degree.
The higher the density, the more likely it is that the network is connected (i.e. that you can reach any node from any other node by following a path along links and intermediate nodes).
The density of a network with N nodes and L links is
\[\begin{align} d = \frac{L}{L_{max}} \end{align}\]
In an undirected network this equals
\[\begin{align} d = \frac{L}{L_{max}} = \frac{2L}{N(N-1)} \end{align}\]
In a directed network this equals
\[\begin{align} d = \frac{L}{L_{max}} = \frac{L}{N(N-1)} \end{align}\]
round(edge_density(G), 2)## [1] 0.17# The density of an undirected network equals 2L / ( N * (N-1) )
# Alternatively: 2 * len(G.edges) / len(G.nodes) / (len(G.nodes)-1)
round( 2 * length(E(G)) / ( length(V(G)) * (length(V(G))-1) ), 2)## [1] 0.17Determine the length of the shortest path between two specific nodes
length(shortest_paths(G, "Frodo", "Arwen", weights = E(G, directed = FALSE)$weight)$vpath[[1]])-1## [1] 2Specify the shortest path between two specific nodes
shortest_paths(G, "Frodo", "Arwen", weights = E(G, directed = FALSE)$weight)$vpath[[1]]## + 3/31 vertices, named, from 670f9cf:
## [1] Frodo Elrond ArwenDetermine whether the network is connected
A node j is reachable from another node i if there is a walk from from i to j. A graph G is connected if every node is reachable from every other.
is_connected(G)## [1] FALSEDetermine the number and size of the connected components
A connected component of a graph G is a maximally connected (i.e. that you can reach any node from any other node by following a path along links and intermediate nodes) subgraph of G.
clusters(G)## $membership
## Aragorn Arathorn Arwen Beregond Bilbo Bill Boromir Celeborn
## 1 1 1 1 1 1 1 2
## Denethor Elendil Elrond Éomer Éowyn Faramir Frodo Galadriel
## 1 1 1 1 1 1 1 2
## Gandalf Gimli Glóin Gollum Isildur Legolas Merry Pippin
## 1 1 1 1 1 1 1 1
## Sam Saruman Sauron Shadowfax Théoden Bombadil Treebeard
## 1 1 1 1 1 1 1
##
## $csize
## [1] 29 2
##
## $no
## [1] 2Determine the average shortest path length of connected components in the graph
A common measure of the distance between nodes in a network is the minimum number of edges needed to traverse from one node to the other. This minimum path is called the shortest path, and its length is called the shortest path length.
We can then define the average shortest path length for the entire network by averaging the shortest path lengths across all pairs of nodes.
#round(mean_distance(G), 2)
c( round(mean_distance(induced_subgraph(G, clusters(G)$membership == 1)), 2),
round(mean_distance(induced_subgraph(G, clusters(G)$membership == 2)), 2) )## [1] 2.13 1.00Determine the diameter of the connected components in the graph
The diameter of a network is the maximum shortest path length across all pairs of nodes. That is, the length of the longest shortest path in the network.
#diameter(G, weights = NA)
c( diameter(induced_subgraph(G, clusters(G)$membership == 1), weights = NA),
diameter(induced_subgraph(G, clusters(G)$membership == 2), weights = NA) )## [1] 4 1Determine the average clustering coefficient of the graph
The local clustering of each node in a graph G is the fraction of triangles that actually exist over all possible triangles in its neighborhood. The average clustering coefficient of a graph G is the mean of local clusterings.
# Global average clustering
round(transitivity(G, type="average",
vids = NULL, # V(conn_comp),
weights = NULL,
isolates = "zero"), 3)## [1] 0.44# Global transitivity (weights nodes with large degree higher than average clustering)
round(transitivity(G, type="global",
vids = NULL, # V(conn_comp),
weights = NULL,
isolates = "zero"), 3)## [1] 0.453Determine the assortativity of the network based on the correlation between degrees of neighbor nodes, as well as a categorical attribute
Nodes (People) in a social network may have a variety of attributes, e.g. age, gender, location, interests, etc. For example, in our LotR network, we have the attributes gender and subtype for each person.
In social networks, it’s often the case that people who are connected to one another tend to share similar attributes. For example, in our LotR network, it may be the case that people who are connected to one another tend to be of the same gender or subtype. This property is called assortativity.
Assortativity based on degree is called degree assortativity, which occurs when high-degree nodes tend to be connected to other high-degree nodes and low-degree nodes tend to be connected to other low-degree nodes. In addition to degree, assortativity can also be based on categorical or numeric attributes.
# Assortativity of the network based on the correlation between degrees of neighbor nodes
round(assortativity_degree(G, directed = FALSE), 2)## [1] -0.26# Assortativity of the network based on subtype, a categorical attribute of the nodes
v_types <- as.numeric(factor(V(G)$subtype))
round(assortativity_nominal(G, types = v_types, directed = FALSE), 2)## [1] 0.16Add gender and subtype attributes and colors to the nodes
Determine the unique genders in the dataset
genders <- network_df %>%
dplyr::filter(source_type == "per") %>%
dplyr::distinct(source_gender) %>%
dplyr::select(source_gender) %>%
dplyr::arrange(source_gender)
genders <- genders$source_gender
genders## [1] "female" "male"# tableau
color_palette <- brewer.pal(n = 8, name = "Set1")
color_palette## [1] "#E41A1C" "#377EB8" "#4DAF4A" "#984EA3" "#FF7F00" "#FFFF33" "#A65628"
## [8] "#F781BF"Associate the unique genders with colors
# qc source: https://www.r-bloggers.com/2018/03/r-tip-use-named-vectors-to-re-map-values/
# tableau: orange, blue
gender_colormap <- qc( "female" = "#e49444" , "male" = "#5778a4" )
gender_colormap ## female male
## "#e49444" "#5778a4"Determine the unique subtypes in the dataset
subtypes <- network_df %>%
dplyr::filter(source_type == "per") %>%
dplyr::distinct(source_subtype) %>%
dplyr::select(source_subtype) %>%
dplyr::arrange(source_subtype)
subtypes <- subtypes$source_subtype
subtypes## [1] "ainur" "animal" "dwarf" "elves" "ents" "hobbit" "men" "orcs"Associate the unique subtypes with colors
# tableau: blue, orange, green, red, purple, brown, pink, cyan
subtype_colormap <- qc( "ainur" = "#5778a4",
"animal" = "#e49444",
"dwarf" = "#6a9f58",
"elves" = "#d1615d",
"ents" = "#a87c9f",
"hobbit" = "#967662",
"men" = "#f1a2a9",
"orcs" = "#17becf" )
subtype_colormap ## ainur animal dwarf elves ents hobbit men orcs
## "#5778a4" "#e49444" "#6a9f58" "#d1615d" "#a87c9f" "#967662" "#f1a2a9" "#17becf"Create a data frame that associates each node (person) with four new attributes for that person
attrs <- network_df %>%
dplyr::filter(source_type == "per", target_type == "per", weight > 20) %>%
dplyr::select(source_name, source_subtype, source_gender) %>%
dplyr::mutate(subtype_color = subtype_colormap[source_subtype],
gender_color = gender_colormap[source_gender]) %>%
dplyr::distinct()
attrs## source_name source_subtype source_gender subtype_color gender_color
## 1 Aragorn men male #f1a2a9 #5778a4
## 2 Arathorn men male #f1a2a9 #5778a4
## 3 Arwen elves female #d1615d #e49444
## 4 Beregond men male #f1a2a9 #5778a4
## 5 Bilbo hobbit male #967662 #5778a4
## 6 Bill animal male #e49444 #5778a4
## 7 Boromir men male #f1a2a9 #5778a4
## 8 Celeborn elves male #d1615d #5778a4
## 9 Denethor men male #f1a2a9 #5778a4
## 10 Elendil men male #f1a2a9 #5778a4
## 11 Elrond elves male #d1615d #5778a4
## 12 Éomer men male #f1a2a9 #5778a4
## 13 Éowyn men female #f1a2a9 #e49444
## 14 Faramir men male #f1a2a9 #5778a4
## 15 Frodo hobbit male #967662 #5778a4
## 16 Galadriel elves female #d1615d #e49444
## 17 Gandalf ainur male #5778a4 #5778a4
## 18 Gimli dwarf male #6a9f58 #5778a4
## 19 Glóin dwarf male #6a9f58 #5778a4
## 20 Gollum hobbit male #967662 #5778a4
## 21 Isildur men male #f1a2a9 #5778a4
## 22 Legolas elves male #d1615d #5778a4
## 23 Merry hobbit male #967662 #5778a4
## 24 Pippin hobbit male #967662 #5778a4
## 25 Sam hobbit male #967662 #5778a4
## 26 Saruman ainur male #5778a4 #5778a4
## 27 Sauron ainur male #5778a4 #5778a4
## 28 Shadowfax animal male #e49444 #5778a4
## 29 Théoden men male #f1a2a9 #5778a4
## 30 Bombadil ainur male #5778a4 #5778a4
## 31 Treebeard ents male #a87c9f #5778a4Assign the attributes to the nodes in the network
V(G)$subtype_color <- attrs$subtype_color
V(G)$gender_color <- attrs$gender_colorCheck that the attributes were added to the nodes
# V(G)
vertex.attributes(G)## $name
## [1] "Aragorn" "Arathorn" "Arwen" "Beregond" "Bilbo" "Bill"
## [7] "Boromir" "Celeborn" "Denethor" "Elendil" "Elrond" "Éomer"
## [13] "Éowyn" "Faramir" "Frodo" "Galadriel" "Gandalf" "Gimli"
## [19] "Glóin" "Gollum" "Isildur" "Legolas" "Merry" "Pippin"
## [25] "Sam" "Saruman" "Sauron" "Shadowfax" "Théoden" "Bombadil"
## [31] "Treebeard"
##
## $type
## [1] "per" "per" "per" "per" "per" "per" "per" "per" "per" "per" "per" "per"
## [13] "per" "per" "per" "per" "per" "per" "per" "per" "per" "per" "per" "per"
## [25] "per" "per" "per" "per" "per" "per" "per"
##
## $subtype
## [1] "men" "men" "elves" "men" "hobbit" "animal" "men" "elves"
## [9] "men" "men" "elves" "men" "men" "men" "hobbit" "elves"
## [17] "ainur" "dwarf" "dwarf" "hobbit" "men" "elves" "hobbit" "hobbit"
## [25] "hobbit" "ainur" "ainur" "animal" "men" "ainur" "ents"
##
## $gender
## [1] "male" "male" "female" "male" "male" "male" "male" "male"
## [9] "male" "male" "male" "male" "female" "male" "male" "female"
## [17] "male" "male" "male" "male" "male" "male" "male" "male"
## [25] "male" "male" "male" "male" "male" "male" "male"
##
## $volume
## [1] "Books 123" "Books 123" "Books 123" "Books 123" "Books 123" "Books 123"
## [7] "Books 123" "Books 123" "Books 123" "Books 123" "Books 123" "Books 123"
## [13] "Books 123" "Books 123" "Books 123" "Books 123" "Books 123" "Books 123"
## [19] "Books 123" "Books 123" "Books 123" "Books 123" "Books 123" "Books 123"
## [25] "Books 123" "Books 123" "Books 123" "Books 123" "Books 123" "Books 123"
## [31] "Books 123"
##
## $subtype_color
## [1] "#f1a2a9" "#f1a2a9" "#d1615d" "#f1a2a9" "#967662" "#e49444" "#f1a2a9"
## [8] "#d1615d" "#f1a2a9" "#f1a2a9" "#d1615d" "#f1a2a9" "#f1a2a9" "#f1a2a9"
## [15] "#967662" "#d1615d" "#5778a4" "#6a9f58" "#6a9f58" "#967662" "#f1a2a9"
## [22] "#d1615d" "#967662" "#967662" "#967662" "#5778a4" "#5778a4" "#e49444"
## [29] "#f1a2a9" "#5778a4" "#a87c9f"
##
## $gender_color
## [1] "#5778a4" "#5778a4" "#e49444" "#5778a4" "#5778a4" "#5778a4" "#5778a4"
## [8] "#5778a4" "#5778a4" "#5778a4" "#5778a4" "#5778a4" "#e49444" "#5778a4"
## [15] "#5778a4" "#e49444" "#5778a4" "#5778a4" "#5778a4" "#5778a4" "#5778a4"
## [22] "#5778a4" "#5778a4" "#5778a4" "#5778a4" "#5778a4" "#5778a4" "#5778a4"
## [29] "#5778a4" "#5778a4" "#5778a4"Check that the undirected edges have weights
# E(G)
edge.attributes(G)## $weight
## [1] 533 181 162 146 127 126 124 123 118 115 109 101 86 84 75 73 72 68 65
## [20] 64 63 63 59 57 55 54 54 51 50 45 44 42 41 40 39 39 36 36
## [39] 36 35 34 34 33 32 32 31 30 29 29 28 28 28 28 27 27 27 27
## [58] 27 26 26 26 26 26 26 25 25 25 24 24 24 24 24 23 22 22 22
## [77] 21 21 21Create a new network graph that only consists of the largest connected component
Determine the largest connected component and
Create a new network graph that only consists of the largest connected component
largest_cc <- (clusters(G)$membership == 1)
conn_comp <- induced_subgraph(G, largest_cc)
conn_comp## IGRAPH 65d568c UNWB 29 78 --
## + attr: name (v/c), type (v/c), subtype (v/c), gender (v/c), volume
## | (v/c), subtype_color (v/c), gender_color (v/c), weight (e/n)
## + edges from 65d568c (vertex names):
## [1] Frodo --Sam Frodo --Gandalf Merry --Pippin Aragorn--Frodo
## [5] Frodo --Gollum Bilbo --Frodo Gandalf--Pippin Aragorn--Gandalf
## [9] Gollum --Sam Frodo --Pippin Gimli --Legolas Pippin --Sam
## [13] Frodo --Merry Aragorn--Legolas Aragorn--Sam Aragorn--Gimli
## [17] Gandalf--Saruman Boromir--Frodo Aragorn--Merry Aragorn--Pippin
## [21] Aragorn--Boromir Merry --Sam Aragorn--Elrond Gandalf--Théoden
## [25] Faramir--Frodo Bilbo --Gandalf Gandalf--Gimli Gandalf--Sam
## + ... omitted several edgesConfirm that the new network graph (conn_comp) is indeed connected
is_connected(conn_comp)## [1] TRUEAnalyze characteristics of the largest connected component of the LotR network
Number of nodes
Sometimes the number of vertices (also called nodes) in a graph is called the order of the graph. We can get the number of nodes in a graph with gorder(G).
# Count the number of nodes
gorder(conn_comp)## [1] 29vcount(conn_comp)## [1] 29List of nodes
# List all of the nodes
V(conn_comp)## + 29/29 vertices, named, from 65d568c:
## [1] Aragorn Arathorn Arwen Beregond Bilbo Bill Boromir
## [8] Denethor Elendil Elrond Éomer Éowyn Faramir Frodo
## [15] Gandalf Gimli Glóin Gollum Isildur Legolas Merry
## [22] Pippin Sam Saruman Sauron Shadowfax Théoden Bombadil
## [29] TreebeardList neighbors of a node
# List neighbors of node "Aragorn"
neighbors(conn_comp, "Aragorn")## + 17/29 vertices, named, from 65d568c:
## [1] Arathorn Arwen Boromir Elendil Elrond Éomer Faramir Frodo
## [9] Gandalf Gimli Legolas Merry Pippin Sam Saruman Sauron
## [17] ThéodenDetermine the degree of each node in the graph
cc_degree <- degree(conn_comp)
# Arrange nodes alphabetically
# cc_degree[sort(names(cc_degree))]
# Arrange nodes in descending order of degree
cc_degree[order(cc_degree, decreasing = TRUE)]## Gandalf Aragorn Frodo Pippin Sam Merry Boromir Faramir
## 18 17 14 11 10 9 7 7
## Gimli Legolas Saruman Treebeard Bilbo Denethor Elrond Éomer
## 7 6 5 5 4 4 4 4
## Sauron Théoden Gollum Arwen Elendil Éowyn Arathorn Beregond
## 4 4 3 2 2 2 1 1
## Bill Glóin Isildur Shadowfax Bombadil
## 1 1 1 1 1cc_degree <- degree(conn_comp)
# Arrange nodes alphabetically
# cc_degree[sort(names(cc_degree))]
# Arrange nodes in descending order of degree
cc_degree_distribution <- cc_degree[order(cc_degree, decreasing = TRUE)]
# Alternatively: tibble::enframe(cc_degree_distribution) # returns columns `name` and `value`
cc_degree_distribution <- data.frame(Character=factor(names(cc_degree_distribution)),
Degree=cc_degree_distribution,
row.names=NULL) %>% arrange(desc(Degree))
ggplot(data = cc_degree_distribution, aes(x = reorder(Character, -Degree), y = Degree)) +
geom_col(aes(fill = Degree)) +
scale_color_distiller(palette = "Blues", direction = 1, aesthetics = c("colour", "fill")) +
scale_y_continuous(breaks=seq(0, 20, 2.5), limits = c(0, 20)) +
# ylim(0, 20) +
labs(title = "Degree Distribution of LotR Characters") +
xlab("Character") +
theme_light() +
theme(legend.position = "none",
panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
plot.title = element_text(hjust = 0.5),
axis.text.x = element_text(angle = 90))
Determine the average degree of the graph
The average degree of a network is
\[\begin{align} \langle k \rangle = \frac{\sum_{i=1} k_i}{N} \end{align}\]
round(mean(degree(conn_comp), na.rm = TRUE), 2)## [1] 5.38# The average degree of an undirected network equals 2L / N
round( 2 * length(E(conn_comp)) / length(V(conn_comp)), 2)## [1] 5.38Number of edges
Sometimes the number of edges (also called links) in a graph is called the size of the graph. We can get the number of edges in a graph with ecount(G).
# Count the number of edges
ecount(conn_comp)## [1] 78List of edges
# List all of the edges
E(conn_comp)## + 78/78 edges from 65d568c (vertex names):
## [1] Frodo --Sam Frodo --Gandalf Merry --Pippin
## [4] Aragorn --Frodo Frodo --Gollum Bilbo --Frodo
## [7] Gandalf --Pippin Aragorn --Gandalf Gollum --Sam
## [10] Frodo --Pippin Gimli --Legolas Pippin --Sam
## [13] Frodo --Merry Aragorn --Legolas Aragorn --Sam
## [16] Aragorn --Gimli Gandalf --Saruman Boromir --Frodo
## [19] Aragorn --Merry Aragorn --Pippin Aragorn --Boromir
## [22] Merry --Sam Aragorn --Elrond Gandalf --Théoden
## [25] Faramir --Frodo Bilbo --Gandalf Gandalf --Gimli
## [28] Gandalf --Sam Aragorn --Éomer Gandalf --Legolas
## + ... omitted several edgesDetermine the density of the largest connected component
The density of a network is the fraction of possible links that actually exist, which is the same as the fraction of pairs of nodes that are actually connected. The average degree of a network is related (directly proportional) to its density. The density is the ratio between the average and maximum degree.
The higher the density, the more likely it is that the network is connected (i.e. that you can reach any node from any other node by following a path along links and intermediate nodes).
The density of a network with N nodes and L links is
\[\begin{align} d = \frac{L}{L_{max}} \end{align}\]
In an undirected network this equals
\[\begin{align} d = \frac{L}{L_{max}} = \frac{2L}{N(N-1)} \end{align}\]
In a directed network this equals
\[\begin{align} d = \frac{L}{L_{max}} = \frac{L}{N(N-1)} \end{align}\]
round(edge_density(conn_comp), 2)## [1] 0.19# The density of an undirected network equals 2L / ( N * (N-1) )
# Alternatively: 2 * len(conn_comp.edges) / len(conn_comp.nodes) / (len(conn_comp.nodes)-1)
round( 2 * length(E(conn_comp)) / ( length(V(conn_comp)) * (length(V(conn_comp))-1) ), 2)## [1] 0.19Determine the length of the shortest path between two specific nodes
length(shortest_paths(conn_comp, "Frodo", "Arwen", weights = E(conn_comp, directed = FALSE)$weight)$vpath[[1]])-1## [1] 2Specify the shortest path between two specific nodes
shortest_paths(conn_comp, "Frodo", "Arwen", weights = E(conn_comp, directed = FALSE)$weight)$vpath[[1]]## + 3/29 vertices, named, from 65d568c:
## [1] Frodo Elrond ArwenDetermine whether the network is connected
A node j is reachable from another node i if there is a walk from from i to j. A graph G is connected if every node is reachable from every other.
is_connected(conn_comp)## [1] TRUEDetermine the number and size of the connected components
A connected component of a graph G is a maximally connected (i.e. that you can reach any node from any other node by following a path along links and intermediate nodes) subgraph of G.
# Count the number of connected components
clusters(conn_comp)## $membership
## Aragorn Arathorn Arwen Beregond Bilbo Bill Boromir Denethor
## 1 1 1 1 1 1 1 1
## Elendil Elrond Éomer Éowyn Faramir Frodo Gandalf Gimli
## 1 1 1 1 1 1 1 1
## Glóin Gollum Isildur Legolas Merry Pippin Sam Saruman
## 1 1 1 1 1 1 1 1
## Sauron Shadowfax Théoden Bombadil Treebeard
## 1 1 1 1 1
##
## $csize
## [1] 29
##
## $no
## [1] 1Determine the average shortest path length of the largest connected component
A common measure of the distance between nodes in a network is the minimum number of edges needed to traverse from one node to the other. This minimum path is called the shortest path, and its length is called the shortest path length.
We can then define the average shortest path length for the entire network by averaging the shortest path lengths across all pairs of nodes.
round(mean_distance(conn_comp), 2)## [1] 2.13Determine the diameter of the largest connected component
The diameter of a network is the maximum shortest path length across all pairs of nodes. That is, the length of the longest shortest path in the network.
diameter(conn_comp, weights = NA)## [1] 4Determine the eccentricity of the nodes in the largest connected component
The eccentricity of a node v is the maximum distance from v to all other nodes in G.
eccentricity(conn_comp)## Aragorn Arathorn Arwen Beregond Bilbo Bill Boromir Denethor
## 2 3 3 4 4 4 3 4
## Elendil Elrond Éomer Éowyn Faramir Frodo Gandalf Gimli
## 3 3 3 4 3 3 3 3
## Glóin Gollum Isildur Legolas Merry Pippin Sam Saruman
## 4 4 4 3 3 3 3 3
## Sauron Shadowfax Théoden Bombadil Treebeard
## 3 4 3 4 4Determine the radius of the largest connected component
The radius is the minimum eccentricity.
radius(conn_comp)## [1] 2Determine the nodes in the center of the largest connected component
The center is the set of nodes with eccentricity equal to radius.
in_center <- (eccentricity(conn_comp) == radius(conn_comp))
eccentricity(conn_comp)[in_center]## Aragorn
## 2Determine the nodes in the periphery of the largest connected component
The periphery is the set of nodes with eccentricity equal to the diameter.
in_periphery <- (eccentricity(conn_comp) == diameter(conn_comp, weights = NA))
eccentricity(conn_comp)[in_periphery]## Beregond Bilbo Bill Denethor Éowyn Glóin Gollum Isildur
## 4 4 4 4 4 4 4 4
## Shadowfax Bombadil Treebeard
## 4 4 4Determine the average clustering coefficient of the graph
The local clustering of each node in a graph G is the fraction of triangles that actually exist over all possible triangles in its neighborhood. The average clustering coefficient of a graph G is the mean of local clusterings.
# Global average clustering
round(transitivity(conn_comp, type="average",
vids = NULL, # V(conn_comp),
weights = NULL,
isolates = "zero"), 3)## [1] 0.471# Global transitivity (weights nodes with large degree higher than average clustering)
round(transitivity(conn_comp, type="global",
vids = NULL, # V(conn_comp),
weights = NULL,
isolates = "zero"), 3)## [1] 0.453Determine the assortativity of the connected component based on the correlation between degrees of neighbor nodes, as well as a categorical attribute
Nodes (People) in a social network may have a variety of attributes, e.g. age, gender, location, interests, etc. For example, in our LotR network, we have the attributes gender and subtype for each person.
In social networks, it’s often the case that people who are connected to one another tend to share similar attributes. For example, in our LotR network, it may be the case that people who are connected to one another tend to be of the same gender or subtype. This property is called assortativity.
Assortativity based on degree is called degree assortativity, which occurs when high-degree nodes tend to be connected to other high-degree nodes and low-degree nodes tend to be connected to other low-degree nodes. In addition to degree, assortativity can also be based on categorical or numeric attributes.
# Assortativity of the connected component based on the correlation between degrees of neighbor nodes
round(assortativity_degree(conn_comp, directed = FALSE), 2)## [1] -0.3# Assortativity of the connected component based on subtype, a categorical attribute of the nodes
v_types <- as.numeric(factor(V(conn_comp)$subtype))
round(assortativity_nominal(conn_comp, types = v_types, directed = FALSE), 2)## [1] 0.14Analyze the nodes of the largest connected component of the LotR network
With social networks, people are often interested in how “important” a particular person is in the network. There are many measures of “importance”.
For instance, in basketball, we might use the number of NBA championships, MVP awards, triple-doubles, points per game, three-pointers, rebounds, assists, etc. to assess “importance”.
Similar to these sports statistics, there are many measures of “importance” in social networks:
- Who has the most connections?
- Who is the ‘closest’ to others in the network?
- Who is most often ‘between’ other pairs of people?
- Who is connected to other ‘important’ people? That is, who has the highest prestige, or rank?
The point isn’t that one of these measures is more important than the others, but rather that each one:
- Captures useful information in a succinct manner
- Encapsulates different information
As Matthew Jackson notes in The Human Network, “Our lives would be simpler if measuring something could always be boiled down to a single statistic. But part of what makes our lives so interesting is that such unidimensional rankings are generally impossible for many of the things that are most important to understand: lists of rankings end up being both controversial and intriguing”.
Degree centrality
In social networks, the number of connections (relationships) a person has is called the person’s “degree”. The associated measure of how central the person is within the network is called the person’s “degree centrality”. In A First Course in Network Science, Menczer, Fortunato, and Davis refer to such high-degree nodes as hubs.
People with higher “degree centrality” have a disproportionate presence and influence in the network (e.g. through the phenomenon known as the “friendship paradox” – that most people have fewer friends than their friends have, on average).
In igraph, you can set the normalized argument equal to TRUE to normalize the degree. If TRUE then the result is divided by n-1, where n is the number of vertices in the graph.
V(conn_comp)$degree_centrality <- degree(conn_comp,
normalized = TRUE)
as_tibble(vertex.attributes(conn_comp)[c("name", "degree_centrality")]) %>%
mutate_if(is.numeric, round, 4) %>%
arrange(desc(degree_centrality))## # A tibble: 29 × 2
## name degree_centrality
## <chr> <dbl>
## 1 Gandalf 0.643
## 2 Aragorn 0.607
## 3 Frodo 0.5
## 4 Pippin 0.393
## 5 Sam 0.357
## 6 Merry 0.321
## 7 Boromir 0.25
## 8 Faramir 0.25
## 9 Gimli 0.25
## 10 Legolas 0.214
## # … with 19 more rowscc_degree_centrality <- degree(conn_comp,
normalized = TRUE)
# Arrange nodes alphabetically
# cc_degree_centrality[sort(names(cc_degree_centrality))]
# Arrange nodes in descending order of degree centrality
cc_degree_centralities <- cc_degree_centrality[order(cc_degree_centrality, decreasing = TRUE)]
# Alternatively: tibble::enframe(cc_degree_centrality) # returns columns `name` and `value`
cc_degree_centralities <- data.frame(Character=factor(names(cc_degree_centrality)),
Centrality=cc_degree_centrality,
row.names=NULL) %>% arrange(desc(Centrality))
ggplot(data = cc_degree_centralities, aes(x = reorder(Character, -Centrality),
y = Centrality)) +
geom_col(aes(fill = Centrality)) +
scale_color_distiller(palette = "Greens",
direction = 1,
aesthetics = c("colour", "fill")) +
scale_y_continuous(breaks=seq(0, 0.7, 0.1)) +
# ylim(0, 1) +
labs(title = "Degree Centralities of LotR Characters") +
xlab("Character") +
theme_light() +
theme(legend.position = "none",
panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
plot.title = element_text(hjust = 0.5),
axis.text.x = element_text(angle = 90))
Eigenvector centrality
Eigenvector centrality is based on the notions of “status” or “prestige” or “rank”. It’s based on the idea that a node is more central if its neighbors are more central. The definitions of this measure are inherently implicit and can be conveyed as eigenvector solutions of linear systems of equations.
One such definition by Bonacich, in which the centrality of a node is proportional to the sum of the cetnrality of its neighbors, is:
\[\begin{align} \lambda C_i^e(g) = \sum_j g_{ij} C_j^e(g) \end{align}\]
where \(C^e(g)\) denotes the eigenvector centrality associated with a network g and \(\lambda\) is a proportionality factor.
When the network is undirected and connected, the largest eigenvalue will be simple and its eigenvector will have entries that are all nonzero and share the same sign. Convention is to report the absolute values of these entries, which will automatically lie between 0 and 1.
# weights = E(conn_comp, directed = FALSE)$weight,
V(conn_comp)$eigenvector_centrality <- eigen_centrality(conn_comp,
directed = FALSE,
weights = NA,
scale = FALSE)$vector # [["vector"]]
as_tibble(vertex.attributes(conn_comp)[c("name", "eigenvector_centrality")]) %>%
mutate_if(is.numeric, round, 4) %>%
arrange(desc(eigenvector_centrality))## # A tibble: 29 × 2
## name eigenvector_centrality
## <chr> <dbl>
## 1 Gandalf 0.400
## 2 Aragorn 0.369
## 3 Frodo 0.343
## 4 Pippin 0.301
## 5 Sam 0.272
## 6 Merry 0.261
## 7 Boromir 0.234
## 8 Faramir 0.234
## 9 Legolas 0.214
## 10 Gimli 0.200
## # … with 19 more rowsV(conn_comp)$eigenvector_centrality <- eigen_centrality(conn_comp,
directed = FALSE,
weights = NA,
scale = FALSE)$vector # [["vector"]]
# Arrange nodes alphabetically
# as_tibble(vertex.attributes(conn_comp)[c("name", "eigenvector_centrality")]) %>%
# arrange(name)
# Arrange nodes in descending order of eigenvector centrality
cc_eigenvector_centralities <- as_tibble(vertex.attributes(conn_comp)[c("name", "eigenvector_centrality")]) %>%
rename(Character = name, Centrality = eigenvector_centrality) %>%
arrange(desc(Centrality))
ggplot(data = cc_eigenvector_centralities, aes(x = reorder(Character, -Centrality),
y = Centrality)) +
geom_col(aes(fill = Centrality)) +
scale_color_distiller(palette = "Blues",
direction = 1,
aesthetics = c("colour", "fill")) +
scale_y_continuous(breaks=seq(0, 0.4, 0.05)) +
# ylim(0, 1) +
labs(title = "Eigenvector Centralities of LotR Characters") +
xlab("Character") +
theme_light() +
theme(legend.position = "none",
panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
plot.title = element_text(hjust = 0.5),
axis.text.x = element_text(angle = 90))
PageRank
PageRank is an algorithm to compute a centrality measure that attempts to capture the “status” or “prestige” or “rank” of each node by imagining people carrying out modified random walk processes (random surfing plus jumping) for a long time and measuring the fraction of times they visit each node. Nodes with many paths leading to them are visited more often by random surfers, and therefore have high PageRank.
PageRank can be computed with an iterative approach called the power method (although there are newer / alternative methods). With the power method, the PageRank of node i at time t is the sum of two terms that convey the two ways one can arrive at node i:
\[\begin{align} R_t(i) = \frac{\alpha}{N} + (1 - \alpha) \sum_{j \in pred(i)} \frac{R_{t-1}(j)}{k_{out}(j)} \end{align}\]
The first term conveys teleportation to node i, which is one of N possible targets of a jump. The second term conveys how someone can travel along one of the edges to node i during the random walk.
The definition is recursive: the PageRank of a node depends on that of its neighbors. For \(\alpha > 0\), PageRank is guaranteed to converge, even in very large networks.
# weights = E(conn_comp,directed = FALSE)$weight
V(conn_comp)$pagerank <- page_rank(conn_comp,
algo = "prpack",
directed = FALSE,
damping = 0.9,
weights = NA)$vector # [["vector"]]
as_tibble(vertex.attributes(conn_comp)[c("name", "pagerank")]) %>%
mutate_if(is.numeric, round, 4) %>%
arrange(desc(pagerank))## # A tibble: 29 × 2
## name pagerank
## <chr> <dbl>
## 1 Gandalf 0.107
## 2 Aragorn 0.106
## 3 Frodo 0.0843
## 4 Pippin 0.0662
## 5 Sam 0.0614
## 6 Merry 0.0543
## 7 Gimli 0.0446
## 8 Boromir 0.0418
## 9 Faramir 0.0418
## 10 Legolas 0.0364
## # … with 19 more rowsV(conn_comp)$pagerank_centrality <- page_rank(conn_comp,
algo = "prpack",
directed = FALSE,
damping = 0.9,
weights = NA)$vector # [["vector"]]
# Arrange nodes alphabetically
# as_tibble(vertex.attributes(conn_comp)[c("name", "pagerank_centrality")]) %>%
# arrange(name)
# Arrange nodes in descending order of pagerank centrality
cc_pagerank_centralities <- as_tibble(vertex.attributes(conn_comp)[c("name", "pagerank_centrality")]) %>%
rename(Character = name, Centrality = pagerank_centrality) %>%
arrange(desc(Centrality))
ggplot(data = cc_pagerank_centralities, aes(x = reorder(Character, -Centrality),
y = Centrality)) +
geom_col(aes(fill = Centrality)) +
scale_color_distiller(palette = "Greys",
direction = 1,
aesthetics = c("colour", "fill")) +
scale_y_continuous(breaks=seq(0, 0.15, 0.02)) +
# ylim(0, 1) +
labs(title = "PageRank Centralities of LotR Characters") +
xlab("Character") +
theme_light() +
theme(legend.position = "none",
panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
plot.title = element_text(hjust = 0.5),
axis.text.x = element_text(angle = 90))
Closeness centrality
The closeness centrality of a node is the inverse of the sum of the distances from the node to all the other nodes.
\[\begin{align} closeness_i = \frac{1}{\sum_{j \ne i} l_{ij}} ; \end{align}\]
Alternatively, by multiplying this definition by N - 1, we discount the network size and make the measure comparable across networks.
\[\begin{align} \bar{closeness_i} = \frac{N - 1}{\sum_{j \ne i} l_{ij}} = \frac{1}{\frac{\sum_{j \ne i} l_{ij}}{(N - 1)}} \end{align}\]
Since the term in the denominator is the average distance from a node to the other nodes, this definition conveys that we can also interpret the node’s closeness centrality as the inverse of its average distance.
# weights = E(conn_comp, directed = FALSE)$weight
V(conn_comp)$closeness_centrality <- closeness(conn_comp,
weights = NA,
normalized = TRUE)
as_tibble(vertex.attributes(conn_comp)[c("name", "closeness_centrality")]) %>%
mutate_if(is.numeric, round, 4) %>%
arrange(desc(closeness_centrality))## # A tibble: 29 × 2
## name closeness_centrality
## <chr> <dbl>
## 1 Aragorn 0.718
## 2 Gandalf 0.718
## 3 Frodo 0.651
## 4 Pippin 0.596
## 5 Merry 0.583
## 6 Sam 0.583
## 7 Boromir 0.538
## 8 Faramir 0.538
## 9 Gimli 0.538
## 10 Legolas 0.538
## # … with 19 more rowsV(conn_comp)$closeness_centrality <- closeness(conn_comp,
weights = NA,
normalized = TRUE)
# Arrange nodes alphabetically
# as_tibble(vertex.attributes(conn_comp)[c("name", "closeness_centrality")]) %>%
# arrange(name)
# Arrange nodes in descending order of closeness centrality
cc_closeness_centralities <- as_tibble(vertex.attributes(conn_comp)[c("name", "closeness_centrality")]) %>%
rename(Character = name, Centrality = closeness_centrality) %>%
arrange(desc(Centrality))
ggplot(data = cc_closeness_centralities, aes(x = reorder(Character, -Centrality),
y = Centrality)) +
geom_col(aes(fill = Centrality)) +
scale_color_distiller(palette = "Purples",
direction = 1,
aesthetics = c("colour", "fill")) +
scale_y_continuous(breaks=seq(0, 0.8, 0.1), limits = c(0, 0.8)) +
# ylim(0, 0.8) +
labs(title = "Closeness Centralities of LotR Characters") +
xlab("Character") +
theme_light() +
theme(legend.position = "none",
panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
plot.title = element_text(hjust = 0.5),
axis.text.x = element_text(angle = 90))
Betweenness centrality
Imagine diffusion processes happening in networks, e.g. information being shared in social networks, products being transported through manufacturing networks, data being transported through communication networks. Suppose these diffusion processes travel from node to node along shortest paths. In this situation, a node is more central (has higher betweenness centrality) when more and more of these diffusion processes (shortest paths) pass through the node.
Specifically, a node’s betweenness centrality is:
\[\begin{align} betweenness_i = \sum_{h \ne j \ne i} \frac{\sigma_{hj}(i)}{\sigma_{hj}} \end{align}\]
where the sum is over all pairs of nodes h and j, not equal to i or each other. If no shortest path between h and j goes through i, the contribution of (h, j) to the betweenness of i is 0. If all shortest paths between h and j go through i, the contribution is 1.
Since the potential contributions come from all pairs of nodes, the betweenness grows with the network size. To normalize \(betweenness_i\) and make the measure comparable across networks, we divide it by \({N - 1 \choose 2}\).
# weights = E(conn_comp, directed = FALSE)$weight,
V(conn_comp)$betweenness_centrality <- betweenness(conn_comp,
directed = FALSE,
weights = NA,
normalized = TRUE)
as_tibble(vertex.attributes(conn_comp)[c("name", "betweenness_centrality")]) %>%
mutate_if(is.numeric, round, 4) %>%
arrange(desc(betweenness_centrality))## # A tibble: 29 × 2
## name betweenness_centrality
## <chr> <dbl>
## 1 Aragorn 0.345
## 2 Gandalf 0.241
## 3 Frodo 0.155
## 4 Sam 0.103
## 5 Pippin 0.0965
## 6 Gimli 0.0763
## 7 Elendil 0.0714
## 8 Merry 0.0628
## 9 Éomer 0.0184
## 10 Elrond 0.0082
## # … with 19 more rowsV(conn_comp)$betweenness_centrality <- betweenness(conn_comp,
directed = FALSE,
weights = NA,
normalized = TRUE)
# Arrange nodes alphabetically
# as_tibble(vertex.attributes(conn_comp)[c("name", "betweenness_centrality")]) %>%
# arrange(name)
# Arrange nodes in descending order of betweenness centrality
cc_betweenness_centralities <- as_tibble(vertex.attributes(conn_comp)[c("name", "betweenness_centrality")]) %>%
rename(Character = name, Centrality = betweenness_centrality) %>%
arrange(desc(Centrality))
ggplot(data = cc_betweenness_centralities, aes(x = reorder(Character, -Centrality),
y = Centrality)) +
geom_col(aes(fill = Centrality)) +
scale_color_distiller(palette = "Oranges",
direction = 1,
aesthetics = c("colour", "fill")) +
scale_y_continuous(breaks=seq(0, 0.35, 0.05), limits = c(0, 0.35)) +
# ylim(0, 1) +
labs(title = "Betweenness Centralities of LotR Characters") +
xlab("Character") +
theme_light() +
theme(legend.position = "none",
panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
plot.title = element_text(hjust = 0.5),
axis.text.x = element_text(angle = 90))
Clustering coefficient (Transitivity)
The clustering coefficient (transitivity) of a node is the fraction of pairs of the node’s neighbors that are connected to each other. In a social network we can rephrase this definition as – the clustering coefficient for a person is the fraction of pairs of the person’s connections that are connected to each other. The connectivity among neighbors of nodes is an important feature of local structure because it indicates the extent to which the nodes are tightly knit, or clustered.
\[\begin{align} clustering_i = \frac{\tau(i)}{\tau_{max}(i)} = \frac{2\tau(i)}{k_i(k_i - 1)} \end{align}\]
where \(\tau(i)\) is the number of triangles involving i. Nodes with degree k < 2 are excluded when calculating the average clustering coefficient.
By averaging the clustering coefficient across the nodes, we can calculate a clustering coefficient for the entire network. A low clustering coefficient (near zero) indicates the network has few triangles, whereas a high clustering coefficient indicates it has many triangles. Social networks tend to have high clustering coefficients.
# weights = E(conn_comp, directed = FALSE)$weight,
V(conn_comp)$clustering_coefficient <- transitivity(conn_comp,
type="local",
vids = NULL, # V(conn_comp),
weights = NULL,
isolates = "zero")
as_tibble(vertex.attributes(conn_comp)[c("name", "clustering_coefficient")]) %>%
mutate_if(is.numeric, round, 4) %>%
arrange(desc(clustering_coefficient))## # A tibble: 29 × 2
## name clustering_coefficient
## <chr> <dbl>
## 1 Arwen 1
## 2 Denethor 1
## 3 Gollum 1
## 4 Legolas 0.933
## 5 Boromir 0.857
## 6 Faramir 0.857
## 7 Bilbo 0.833
## 8 Sauron 0.833
## 9 Théoden 0.833
## 10 Elrond 0.667
## # … with 19 more rows# weights = E(conn_comp, directed = FALSE)$weight,
V(conn_comp)$clustering_coefficient <- transitivity(conn_comp,
type="local",
vids = NULL,
weights = NULL,
isolates = "zero")
# Arrange nodes alphabetically
# as_tibble(vertex.attributes(conn_comp)[c("name", "clustering_coefficient")]) %>%
# arrange(name)
# Arrange nodes in descending order of clustering centrality
cc_clustering_coefficients <- as_tibble(vertex.attributes(conn_comp)[c("name", "clustering_coefficient")]) %>%
rename(Character = name, Centrality = clustering_coefficient) %>%
arrange(desc(Centrality))
ggplot(data = cc_clustering_coefficients, aes(x = reorder(Character, -Centrality),
y = Centrality)) +
geom_col(aes(fill = Centrality)) +
scale_color_distiller(palette = "Reds",
direction = 1,
aesthetics = c("colour", "fill")) +
scale_y_continuous(breaks=seq(0, 1.0, 0.2), limits = c(0, 1.0)) +
# ylim(0, 1.2) +
labs(title = "Clustering Centralities of LotR Characters") +
xlab("Character") +
theme_light() +
theme(legend.position = "none",
panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
plot.title = element_text(hjust = 0.5),
axis.text.x = element_text(angle = 90))
Remove attributes, if necessary
# Check attributes
vertex.attributes(conn_comp)## $name
## [1] "Aragorn" "Arathorn" "Arwen" "Beregond" "Bilbo" "Bill"
## [7] "Boromir" "Denethor" "Elendil" "Elrond" "Éomer" "Éowyn"
## [13] "Faramir" "Frodo" "Gandalf" "Gimli" "Glóin" "Gollum"
## [19] "Isildur" "Legolas" "Merry" "Pippin" "Sam" "Saruman"
## [25] "Sauron" "Shadowfax" "Théoden" "Bombadil" "Treebeard"
##
## $type
## [1] "per" "per" "per" "per" "per" "per" "per" "per" "per" "per" "per" "per"
## [13] "per" "per" "per" "per" "per" "per" "per" "per" "per" "per" "per" "per"
## [25] "per" "per" "per" "per" "per"
##
## $subtype
## [1] "men" "men" "elves" "men" "hobbit" "animal" "men" "men"
## [9] "men" "elves" "men" "men" "men" "hobbit" "ainur" "dwarf"
## [17] "dwarf" "hobbit" "men" "elves" "hobbit" "hobbit" "hobbit" "ainur"
## [25] "ainur" "animal" "men" "ainur" "ents"
##
## $gender
## [1] "male" "male" "female" "male" "male" "male" "male" "male"
## [9] "male" "male" "male" "female" "male" "male" "male" "male"
## [17] "male" "male" "male" "male" "male" "male" "male" "male"
## [25] "male" "male" "male" "male" "male"
##
## $volume
## [1] "Books 123" "Books 123" "Books 123" "Books 123" "Books 123" "Books 123"
## [7] "Books 123" "Books 123" "Books 123" "Books 123" "Books 123" "Books 123"
## [13] "Books 123" "Books 123" "Books 123" "Books 123" "Books 123" "Books 123"
## [19] "Books 123" "Books 123" "Books 123" "Books 123" "Books 123" "Books 123"
## [25] "Books 123" "Books 123" "Books 123" "Books 123" "Books 123"
##
## $subtype_color
## [1] "#f1a2a9" "#f1a2a9" "#d1615d" "#f1a2a9" "#967662" "#e49444" "#f1a2a9"
## [8] "#f1a2a9" "#f1a2a9" "#d1615d" "#f1a2a9" "#f1a2a9" "#f1a2a9" "#967662"
## [15] "#5778a4" "#6a9f58" "#6a9f58" "#967662" "#f1a2a9" "#d1615d" "#967662"
## [22] "#967662" "#967662" "#5778a4" "#5778a4" "#e49444" "#f1a2a9" "#5778a4"
## [29] "#a87c9f"
##
## $gender_color
## [1] "#5778a4" "#5778a4" "#e49444" "#5778a4" "#5778a4" "#5778a4" "#5778a4"
## [8] "#5778a4" "#5778a4" "#5778a4" "#5778a4" "#e49444" "#5778a4" "#5778a4"
## [15] "#5778a4" "#5778a4" "#5778a4" "#5778a4" "#5778a4" "#5778a4" "#5778a4"
## [22] "#5778a4" "#5778a4" "#5778a4" "#5778a4" "#5778a4" "#5778a4" "#5778a4"
## [29] "#5778a4"
##
## $degree_centrality
## [1] 0.60714286 0.03571429 0.07142857 0.03571429 0.14285714 0.03571429
## [7] 0.25000000 0.14285714 0.07142857 0.14285714 0.14285714 0.07142857
## [13] 0.25000000 0.50000000 0.64285714 0.25000000 0.03571429 0.10714286
## [19] 0.03571429 0.21428571 0.32142857 0.39285714 0.35714286 0.17857143
## [25] 0.14285714 0.03571429 0.14285714 0.03571429 0.17857143
##
## $eigenvector_centrality
## [1] 0.368560552 0.042028641 0.057235334 0.034365889 0.125421977 0.030996562
## [7] 0.234095530 0.133409500 0.042582377 0.133351610 0.105562137 0.041807968
## [13] 0.234095530 0.343251321 0.400349229 0.200451731 0.022858425 0.084441517
## [19] 0.004855863 0.213819354 0.261063274 0.301363798 0.271817262 0.133865003
## [25] 0.142090041 0.045653649 0.114985259 0.039142514 0.147913436
##
## $pagerank
## [1] 0.106087723 0.009064685 0.015053442 0.008863824 0.025809283 0.008971643
## [7] 0.041768216 0.024962005 0.020450644 0.026616700 0.027054331 0.014966407
## [13] 0.041768216 0.084313955 0.107155663 0.044596240 0.009182078 0.020198914
## [19] 0.012651066 0.036422907 0.054309063 0.066190027 0.061370745 0.031661721
## [25] 0.025541760 0.008806059 0.026208802 0.008868459 0.031085425
##
## $pagerank_centrality
## [1] 0.106087723 0.009064685 0.015053442 0.008863824 0.025809283 0.008971643
## [7] 0.041768216 0.024962005 0.020450644 0.026616700 0.027054331 0.014966407
## [13] 0.041768216 0.084313955 0.107155663 0.044596240 0.009182078 0.020198914
## [19] 0.012651066 0.036422907 0.054309063 0.066190027 0.061370745 0.031661721
## [25] 0.025541760 0.008806059 0.026208802 0.008868459 0.031085425
##
## $closeness_centrality
## [1] 0.7179487 0.4242424 0.4307692 0.3783784 0.4666667 0.3733333 0.5384615
## [8] 0.4516129 0.4375000 0.4912281 0.4827586 0.3888889 0.5384615 0.6511628
## [15] 0.7179487 0.5384615 0.3544304 0.4179104 0.3076923 0.5384615 0.5833333
## [22] 0.5957447 0.5833333 0.4827586 0.4912281 0.4242424 0.4827586 0.4000000
## [29] 0.4745763
##
## $betweenness_centrality
## [1] 0.3448979592 0.0000000000 0.0000000000 0.0000000000 0.0038874192
## [6] 0.0000000000 0.0064079953 0.0000000000 0.0714285714 0.0082010582
## [11] 0.0183988410 0.0008818342 0.0064079953 0.1553266986 0.2414367599
## [16] 0.0763007055 0.0000000000 0.0000000000 0.0000000000 0.0017636684
## [21] 0.0628180902 0.0964936592 0.1034087092 0.0060846561 0.0022045855
## [26] 0.0000000000 0.0013227513 0.0000000000 0.0066137566
##
## $clustering_coefficient
## [1] 0.2794118 0.0000000 1.0000000 0.0000000 0.8333333 0.0000000 0.8571429
## [8] 1.0000000 0.0000000 0.6666667 0.5000000 0.0000000 0.8571429 0.3846154
## [15] 0.3006536 0.5714286 0.0000000 1.0000000 0.0000000 0.9333333 0.5833333
## [22] 0.5090909 0.5111111 0.6000000 0.8333333 0.0000000 0.8333333 0.0000000
## [29] 0.6000000# Remove specific attributes
#vertex_attr(conn_comp)["transitivity"] <- NULLPlot the nodes and weighted edges of the largest connected LotR network
(including the names of the characters)
e.size <- 4 * E(conn_comp)$weight / max( E(conn_comp)$weight, na.rm = TRUE )
v.label <- V(conn_comp)$name
set.seed(10)
igraph_options(vertex.size=5,
vertex.color="blue",
vertex.frame.color="blue",
vertex.label=v.label,
vertex.label.dist=1.1,
vertex.label.cex=0.75,
edge.width=e.size,
edge.color="blue")
par(mfrow=c(1,1))
plot(conn_comp, layout=layout_nicely)
title("LotR network")
Plot the nodes and edges of the LotR network (color the nodes by gender)
e.size <- 4 * E(conn_comp)$weight / max( E(conn_comp)$weight, na.rm = TRUE )
v.label <- V(conn_comp)$name
v.color <- V(conn_comp)$gender_color
set.seed(10)
igraph_options(vertex.size=5,
vertex.color=v.color,
vertex.frame.color=v.color,
vertex.label=v.label,
vertex.label.dist=1.1,
vertex.label.cex=0.75,
edge.width=e.size,
edge.color="grey")
par(mfrow=c(1,1))
plot(conn_comp, layout=layout_nicely)
title("LotR network")
Plot the nodes and edges of the LotR network (color the nodes by subtype)
e.size <- 4 * E(conn_comp)$weight / max( E(conn_comp)$weight, na.rm = TRUE )
v.label <- V(conn_comp)$name
v.color <- V(conn_comp)$subtype_color
set.seed(10)
igraph_options(vertex.size=5,
vertex.color=v.color,
vertex.frame.color=v.color,
vertex.label=v.label,
vertex.label.dist=1.1,
vertex.label.cex=0.75,
edge.width=e.size,
edge.color="grey")
par(mfrow=c(1,1))
plot(conn_comp, layout=layout_nicely)
title("LotR network")
Create a network graph for LotR Book 1
book1_df <- sqldf::sqldf("
SELECT
sour.id AS source_id, sour.label as source_name, sour.type AS source_type, sour.subtype AS source_subtype, sour.gender AS source_gender,
dest.id AS target_id, dest.label AS target_name, dest.type AS target_type, dest.subtype AS target_subtype, dest.gender AS target_gender,
conn.weight, conn.volume, conn.title, conn.publication_date
FROM
book1 conn
JOIN ontology sour
ON
conn.source = sour.id
JOIN ontology dest
ON
conn.target = dest.id
UNION
SELECT
dest.id AS source_id, dest.label as source_name, dest.type AS source_type, dest.subtype AS source_subtype, dest.gender AS source_gender,
sour.id AS target_id, sour.label AS target_name, sour.type AS target_type, sour.subtype AS target_subtype, sour.gender AS target_gender,
conn.weight, conn.volume, conn.title, conn.publication_date
FROM
book1 conn
JOIN ontology sour
ON
conn.source = sour.id
JOIN ontology dest
ON
conn.target = dest.id"
)
book1_df %>%
dplyr::mutate("weight" = as.double(weight),
"publication_date" = as.character(publication_date)) %>%
dplyr::arrange(desc(weight)) %>%
head(10)## source_id source_name source_type source_subtype source_gender target_id
## 1 frod Frodo per hobbit male sams
## 2 sams Sam per hobbit male frod
## 3 frod Frodo per hobbit male ganda
## 4 ganda Gandalf per ainur male frod
## 5 arag Aragorn per men male frod
## 6 frod Frodo per hobbit male arag
## 7 bilb Bilbo per hobbit male frod
## 8 frod Frodo per hobbit male bilb
## 9 frod Frodo per hobbit male pipp
## 10 pipp Pippin per hobbit male frod
## target_name target_type target_subtype target_gender weight volume
## 1 Sam per hobbit male 171 Book 1
## 2 Frodo per hobbit male 171 Book 1
## 3 Gandalf per ainur male 129 Book 1
## 4 Frodo per hobbit male 129 Book 1
## 5 Frodo per hobbit male 105 Book 1
## 6 Aragorn per men male 105 Book 1
## 7 Frodo per hobbit male 96 Book 1
## 8 Bilbo per hobbit male 96 Book 1
## 9 Pippin per hobbit male 80 Book 1
## 10 Frodo per hobbit male 80 Book 1
## title publication_date
## 1 The Fellowship of the Ring 1954-07-29
## 2 The Fellowship of the Ring 1954-07-29
## 3 The Fellowship of the Ring 1954-07-29
## 4 The Fellowship of the Ring 1954-07-29
## 5 The Fellowship of the Ring 1954-07-29
## 6 The Fellowship of the Ring 1954-07-29
## 7 The Fellowship of the Ring 1954-07-29
## 8 The Fellowship of the Ring 1954-07-29
## 9 The Fellowship of the Ring 1954-07-29
## 10 The Fellowship of the Ring 1954-07-29book1_edges <- sqldf::sqldf("
SELECT
sour.label as source_name, sour.type as source_type,
dest.label AS target_name, dest.type AS target_type,
conn.weight
FROM
book1 conn
JOIN ontology sour
ON
conn.source = sour.id
JOIN ontology dest
ON
conn.target = dest.id"
) %>%
dplyr::filter(source_type == "per", target_type == "per", weight > 20) %>%
dplyr::select(source_name, target_name, weight) %>%
dplyr::rename(from = source_name, to = target_name)
book1_nodes <- book1_df %>%
dplyr::filter(source_type == "per", target_type == "per", weight > 20) %>%
dplyr::select(source_name, source_type, source_subtype, source_gender, volume, title, publication_date) %>%
dplyr::mutate(publication_date = as.character(publication_date)) %>%
dplyr::rename(name = source_name, type = source_type, subtype = source_subtype, gender = source_gender) %>%
dplyr::distinct()
G_book1 <- graph_from_data_frame(book1_edges, directed = FALSE, vertices = book1_nodes)
#print_all(G_book1)
G_book1## IGRAPH 577ee4e UNWB 12 24 --
## + attr: name (v/c), type (v/c), subtype (v/c), gender (v/c), volume
## | (v/c), title (v/c), publication_date (v/c), weight (e/n)
## + edges from 577ee4e (vertex names):
## [1] Frodo --Sam Frodo --Gandalf Aragorn--Frodo Bilbo --Frodo
## [5] Frodo --Pippin Pippin --Sam Frodo --Merry Merry --Pippin
## [9] Aragorn--Sam Bilbo --Gandalf Merry --Sam Boromir--Frodo
## [13] Aragorn--Gandalf Aragorn--Boromir Gandalf--Sam Aragorn--Merry
## [17] Elrond --Frodo Elrond --Gandalf Aragorn--Elrond Aragorn--Pippin
## [21] Gimli --Legolas Bilbo --Sam Frodo --Legolas Frodo --BombadilCheck that the attributes were added to the nodes
vertex.attributes(G_book1)## $name
## [1] "Aragorn" "Bilbo" "Boromir" "Elrond" "Frodo" "Gandalf"
## [7] "Gimli" "Legolas" "Merry" "Pippin" "Sam" "Bombadil"
##
## $type
## [1] "per" "per" "per" "per" "per" "per" "per" "per" "per" "per" "per" "per"
##
## $subtype
## [1] "men" "hobbit" "men" "elves" "hobbit" "ainur" "dwarf" "elves"
## [9] "hobbit" "hobbit" "hobbit" "ainur"
##
## $gender
## [1] "male" "male" "male" "male" "male" "male" "male" "male" "male" "male"
## [11] "male" "male"
##
## $volume
## [1] "Book 1" "Book 1" "Book 1" "Book 1" "Book 1" "Book 1" "Book 1" "Book 1"
## [9] "Book 1" "Book 1" "Book 1" "Book 1"
##
## $title
## [1] "The Fellowship of the Ring" "The Fellowship of the Ring"
## [3] "The Fellowship of the Ring" "The Fellowship of the Ring"
## [5] "The Fellowship of the Ring" "The Fellowship of the Ring"
## [7] "The Fellowship of the Ring" "The Fellowship of the Ring"
## [9] "The Fellowship of the Ring" "The Fellowship of the Ring"
## [11] "The Fellowship of the Ring" "The Fellowship of the Ring"
##
## $publication_date
## [1] "1954-07-29" "1954-07-29" "1954-07-29" "1954-07-29" "1954-07-29"
## [6] "1954-07-29" "1954-07-29" "1954-07-29" "1954-07-29" "1954-07-29"
## [11] "1954-07-29" "1954-07-29"Check that the undirected edges have weights
E(G_book1)## + 24/24 edges from 577ee4e (vertex names):
## [1] Frodo --Sam Frodo --Gandalf Aragorn--Frodo Bilbo --Frodo
## [5] Frodo --Pippin Pippin --Sam Frodo --Merry Merry --Pippin
## [9] Aragorn--Sam Bilbo --Gandalf Merry --Sam Boromir--Frodo
## [13] Aragorn--Gandalf Aragorn--Boromir Gandalf--Sam Aragorn--Merry
## [17] Elrond --Frodo Elrond --Gandalf Aragorn--Elrond Aragorn--Pippin
## [21] Gimli --Legolas Bilbo --Sam Frodo --Legolas Frodo --Bombadiledge.attributes(G_book1)## $weight
## [1] 171 129 105 96 80 72 64 57 50 44 43 42 41 40 31 30 27 27 22
## [20] 22 22 21 21 21Identify the largest connected component
book1_largest_cc <- clusters(G_book1)$membership == 1
G_book1_cc <- induced_subgraph(G_book1, book1_largest_cc)
G_book1_cc## IGRAPH 44dd484 UNWB 12 24 --
## + attr: name (v/c), type (v/c), subtype (v/c), gender (v/c), volume
## | (v/c), title (v/c), publication_date (v/c), weight (e/n)
## + edges from 44dd484 (vertex names):
## [1] Frodo --Sam Frodo --Gandalf Aragorn--Frodo Bilbo --Frodo
## [5] Frodo --Pippin Pippin --Sam Frodo --Merry Merry --Pippin
## [9] Aragorn--Sam Bilbo --Gandalf Merry --Sam Boromir--Frodo
## [13] Aragorn--Gandalf Aragorn--Boromir Gandalf--Sam Aragorn--Merry
## [17] Elrond --Frodo Elrond --Gandalf Aragorn--Elrond Aragorn--Pippin
## [21] Gimli --Legolas Bilbo --Sam Frodo --Legolas Frodo --BombadilAdd centrality measures to nodes in the largest connected component
V(G_book1_cc)$degree_centrality <- degree(G_book1_cc,
normalized = TRUE)
# weights = E(G_book1_cc, directed = FALSE)$weight,
V(G_book1_cc)$clustering_centrality <- transitivity(G_book1_cc,
type="local",
vids = NULL, # V(G_book1_cc),
weights = NA,
isolates = 'zero')
V(G_book1_cc)$closeness_centrality <- closeness(G_book1_cc,
weights = NA,
normalized = TRUE)
V(G_book1_cc)$betweenness_centrality <- betweenness(G_book1_cc,
directed = FALSE,
weights = NA,
normalized = TRUE)
V(G_book1_cc)$eigenvector_centrality <- eigen_centrality(G_book1_cc,
directed = FALSE,
weights = NA,
scale = FALSE)[["vector"]]
V(G_book1_cc)$pagerank_centrality <- page_rank(G_book1_cc,
algo = "prpack",
directed = FALSE,
damping = 0.9,
weights = NA)[["vector"]]
vertex.attributes(G_book1_cc)## $name
## [1] "Aragorn" "Bilbo" "Boromir" "Elrond" "Frodo" "Gandalf"
## [7] "Gimli" "Legolas" "Merry" "Pippin" "Sam" "Bombadil"
##
## $type
## [1] "per" "per" "per" "per" "per" "per" "per" "per" "per" "per" "per" "per"
##
## $subtype
## [1] "men" "hobbit" "men" "elves" "hobbit" "ainur" "dwarf" "elves"
## [9] "hobbit" "hobbit" "hobbit" "ainur"
##
## $gender
## [1] "male" "male" "male" "male" "male" "male" "male" "male" "male" "male"
## [11] "male" "male"
##
## $volume
## [1] "Book 1" "Book 1" "Book 1" "Book 1" "Book 1" "Book 1" "Book 1" "Book 1"
## [9] "Book 1" "Book 1" "Book 1" "Book 1"
##
## $title
## [1] "The Fellowship of the Ring" "The Fellowship of the Ring"
## [3] "The Fellowship of the Ring" "The Fellowship of the Ring"
## [5] "The Fellowship of the Ring" "The Fellowship of the Ring"
## [7] "The Fellowship of the Ring" "The Fellowship of the Ring"
## [9] "The Fellowship of the Ring" "The Fellowship of the Ring"
## [11] "The Fellowship of the Ring" "The Fellowship of the Ring"
##
## $publication_date
## [1] "1954-07-29" "1954-07-29" "1954-07-29" "1954-07-29" "1954-07-29"
## [6] "1954-07-29" "1954-07-29" "1954-07-29" "1954-07-29" "1954-07-29"
## [11] "1954-07-29" "1954-07-29"
##
## $degree_centrality
## [1] 0.63636364 0.27272727 0.18181818 0.27272727 0.90909091 0.45454545
## [7] 0.09090909 0.18181818 0.36363636 0.36363636 0.54545455 0.09090909
##
## $clustering_centrality
## [1] 0.5238095 1.0000000 1.0000000 1.0000000 0.2888889 0.7000000 0.0000000
## [8] 0.0000000 1.0000000 1.0000000 0.6666667 0.0000000
##
## $closeness_centrality
## [1] 0.6875000 0.5500000 0.5238095 0.5500000 0.9166667 0.6111111 0.3666667
## [8] 0.5500000 0.5789474 0.5789474 0.6470588 0.5000000
##
## $betweenness_centrality
## [1] 0.08181818 0.00000000 0.00000000 0.00000000 0.60606061 0.02121212
## [7] 0.00000000 0.18181818 0.00000000 0.00000000 0.03636364 0.00000000
##
## $eigenvector_centrality
## [1] 0.41692398 0.22725633 0.17004595 0.23252534 0.48260060 0.33050919
## [7] 0.01788539 0.09461177 0.30037499 0.30037499 0.38905148 0.09123072
##
## $pagerank_centrality
## [1] 0.13610289 0.06187892 0.04416263 0.06193728 0.20367056 0.09874807
## [7] 0.03417141 0.05741796 0.07948802 0.07948802 0.11627056 0.02666368Convert G_book1 into JSON
G_book1_json <- d3r::d3_igraph(as.undirected(G_book1_cc))
G_book1_json## {"nodes":[{"name":"Aragorn","type":"per","subtype":"men","gender":"male","volume":"Book 1","title":"The Fellowship of the Ring","publication_date":"1954-07-29","degree_centrality":0.6364,"clustering_centrality":0.5238,"closeness_centrality":0.6875,"betweenness_centrality":0.0818,"eigenvector_centrality":0.4169,"pagerank_centrality":0.1361,"id":"Aragorn","_row":"Aragorn"},{"name":"Bilbo","type":"per","subtype":"hobbit","gender":"male","volume":"Book 1","title":"The Fellowship of the Ring","publication_date":"1954-07-29","degree_centrality":0.2727,"clustering_centrality":1,"closeness_centrality":0.55,"betweenness_centrality":0,"eigenvector_centrality":0.2273,"pagerank_centrality":0.0619,"id":"Bilbo","_row":"Bilbo"},{"name":"Boromir","type":"per","subtype":"men","gender":"male","volume":"Book 1","title":"The Fellowship of the Ring","publication_date":"1954-07-29","degree_centrality":0.1818,"clustering_centrality":1,"closeness_centrality":0.5238,"betweenness_centrality":0,"eigenvector_centrality":0.17,"pagerank_centrality":0.0442,"id":"Boromir","_row":"Boromir"},{"name":"Elrond","type":"per","subtype":"elves","gender":"male","volume":"Book 1","title":"The Fellowship of the Ring","publication_date":"1954-07-29","degree_centrality":0.2727,"clustering_centrality":1,"closeness_centrality":0.55,"betweenness_centrality":0,"eigenvector_centrality":0.2325,"pagerank_centrality":0.0619,"id":"Elrond","_row":"Elrond"},{"name":"Frodo","type":"per","subtype":"hobbit","gender":"male","volume":"Book 1","title":"The Fellowship of the Ring","publication_date":"1954-07-29","degree_centrality":0.9091,"clustering_centrality":0.2889,"closeness_centrality":0.9167,"betweenness_centrality":0.6061,"eigenvector_centrality":0.4826,"pagerank_centrality":0.2037,"id":"Frodo","_row":"Frodo"},{"name":"Gandalf","type":"per","subtype":"ainur","gender":"male","volume":"Book 1","title":"The Fellowship of the Ring","publication_date":"1954-07-29","degree_centrality":0.4545,"clustering_centrality":0.7,"closeness_centrality":0.6111,"betweenness_centrality":0.0212,"eigenvector_centrality":0.3305,"pagerank_centrality":0.0987,"id":"Gandalf","_row":"Gandalf"},{"name":"Gimli","type":"per","subtype":"dwarf","gender":"male","volume":"Book 1","title":"The Fellowship of the Ring","publication_date":"1954-07-29","degree_centrality":0.0909,"clustering_centrality":0,"closeness_centrality":0.3667,"betweenness_centrality":0,"eigenvector_centrality":0.0179,"pagerank_centrality":0.0342,"id":"Gimli","_row":"Gimli"},{"name":"Legolas","type":"per","subtype":"elves","gender":"male","volume":"Book 1","title":"The Fellowship of the Ring","publication_date":"1954-07-29","degree_centrality":0.1818,"clustering_centrality":0,"closeness_centrality":0.55,"betweenness_centrality":0.1818,"eigenvector_centrality":0.0946,"pagerank_centrality":0.0574,"id":"Legolas","_row":"Legolas"},{"name":"Merry","type":"per","subtype":"hobbit","gender":"male","volume":"Book 1","title":"The Fellowship of the Ring","publication_date":"1954-07-29","degree_centrality":0.3636,"clustering_centrality":1,"closeness_centrality":0.5789,"betweenness_centrality":0,"eigenvector_centrality":0.3004,"pagerank_centrality":0.0795,"id":"Merry","_row":"Merry"},{"name":"Pippin","type":"per","subtype":"hobbit","gender":"male","volume":"Book 1","title":"The Fellowship of the Ring","publication_date":"1954-07-29","degree_centrality":0.3636,"clustering_centrality":1,"closeness_centrality":0.5789,"betweenness_centrality":0,"eigenvector_centrality":0.3004,"pagerank_centrality":0.0795,"id":"Pippin","_row":"Pippin"},{"name":"Sam","type":"per","subtype":"hobbit","gender":"male","volume":"Book 1","title":"The Fellowship of the Ring","publication_date":"1954-07-29","degree_centrality":0.5455,"clustering_centrality":0.6667,"closeness_centrality":0.6471,"betweenness_centrality":0.0364,"eigenvector_centrality":0.3891,"pagerank_centrality":0.1163,"id":"Sam","_row":"Sam"},{"name":"Bombadil","type":"per","subtype":"ainur","gender":"male","volume":"Book 1","title":"The Fellowship of the Ring","publication_date":"1954-07-29","degree_centrality":0.0909,"clustering_centrality":0,"closeness_centrality":0.5,"betweenness_centrality":0,"eigenvector_centrality":0.0912,"pagerank_centrality":0.0267,"id":"Bombadil","_row":"Bombadil"}],"links":[{"source":"Frodo","target":"Sam","weight":171},{"source":"Frodo","target":"Gandalf","weight":129},{"source":"Aragorn","target":"Frodo","weight":105},{"source":"Bilbo","target":"Frodo","weight":96},{"source":"Frodo","target":"Pippin","weight":80},{"source":"Pippin","target":"Sam","weight":72},{"source":"Frodo","target":"Merry","weight":64},{"source":"Merry","target":"Pippin","weight":57},{"source":"Aragorn","target":"Sam","weight":50},{"source":"Bilbo","target":"Gandalf","weight":44},{"source":"Merry","target":"Sam","weight":43},{"source":"Boromir","target":"Frodo","weight":42},{"source":"Aragorn","target":"Gandalf","weight":41},{"source":"Aragorn","target":"Boromir","weight":40},{"source":"Gandalf","target":"Sam","weight":31},{"source":"Aragorn","target":"Merry","weight":30},{"source":"Elrond","target":"Frodo","weight":27},{"source":"Elrond","target":"Gandalf","weight":27},{"source":"Aragorn","target":"Elrond","weight":22},{"source":"Aragorn","target":"Pippin","weight":22},{"source":"Gimli","target":"Legolas","weight":22},{"source":"Bilbo","target":"Sam","weight":21},{"source":"Frodo","target":"Legolas","weight":21},{"source":"Frodo","target":"Bombadil","weight":21}],"attributes":{}}# jsonlite::minify(G_book1_json)
# jsonlite::prettify(G_book1_json, indent = 4)Write G_book1 to JSON
write(G_book1_json, file = "data/LotR_Book1_from_R.json")Create a network graph for LotR Book 2
book2_df <- sqldf::sqldf("
SELECT
sour.id AS source_id, sour.label as source_name, sour.type AS source_type, sour.subtype AS source_subtype, sour.gender AS source_gender,
dest.id AS target_id, dest.label AS target_name, dest.type AS target_type, dest.subtype AS target_subtype, dest.gender AS target_gender,
conn.weight, conn.volume, conn.title, conn.publication_date
FROM
book2 conn
JOIN ontology sour
ON
conn.source = sour.id
JOIN ontology dest
ON
conn.target = dest.id
UNION
SELECT
dest.id AS source_id, dest.label as source_name, dest.type AS source_type, dest.subtype AS source_subtype, dest.gender AS source_gender,
sour.id AS target_id, sour.label AS target_name, sour.type AS target_type, sour.subtype AS target_subtype, sour.gender AS target_gender,
conn.weight, conn.volume, conn.title, conn.publication_date
FROM
book2 conn
JOIN ontology sour
ON
conn.source = sour.id
JOIN ontology dest
ON
conn.target = dest.id"
)
book2_df %>%
dplyr::mutate("weight" = as.double(weight),
"publication_date" = as.character(publication_date)) %>%
dplyr::arrange(desc(weight)) %>%
head(10)## source_id source_name source_type source_subtype source_gender target_id
## 1 frod Frodo per hobbit male sams
## 2 sams Sam per hobbit male frod
## 3 goll Gollum per hobbit male sams
## 4 sams Sam per hobbit male goll
## 5 frod Frodo per hobbit male goll
## 6 goll Gollum per hobbit male frod
## 7 merr Merry per hobbit male pipp
## 8 pipp Pippin per hobbit male merr
## 9 gimli Gimli per dwarf male lego
## 10 lego Legolas per elves male gimli
## target_name target_type target_subtype target_gender weight volume
## 1 Sam per hobbit male 158 Book 2
## 2 Frodo per hobbit male 158 Book 2
## 3 Sam per hobbit male 101 Book 2
## 4 Gollum per hobbit male 101 Book 2
## 5 Gollum per hobbit male 99 Book 2
## 6 Frodo per hobbit male 99 Book 2
## 7 Pippin per hobbit male 51 Book 2
## 8 Merry per hobbit male 51 Book 2
## 9 Legolas per elves male 50 Book 2
## 10 Gimli per dwarf male 50 Book 2
## title publication_date
## 1 The Two Towers 1954-11-11
## 2 The Two Towers 1954-11-11
## 3 The Two Towers 1954-11-11
## 4 The Two Towers 1954-11-11
## 5 The Two Towers 1954-11-11
## 6 The Two Towers 1954-11-11
## 7 The Two Towers 1954-11-11
## 8 The Two Towers 1954-11-11
## 9 The Two Towers 1954-11-11
## 10 The Two Towers 1954-11-11book2_edges <- sqldf::sqldf("
SELECT
sour.label as source_name, sour.type as source_type,
dest.label AS target_name, dest.type AS target_type,
conn.weight
FROM
book2 conn
JOIN ontology sour
ON
conn.source = sour.id
JOIN ontology dest
ON
conn.target = dest.id"
) %>%
dplyr::filter(source_type == "per", target_type == "per", weight > 20) %>%
dplyr::select(source_name, target_name, weight) %>%
dplyr::rename(from = source_name, to = target_name)
book2_nodes <- book2_df %>%
dplyr::filter(source_type == "per", target_type == "per", weight > 20) %>%
dplyr::select(source_name, source_type, source_subtype, source_gender, volume, title, publication_date) %>%
dplyr::mutate(publication_date = as.character(publication_date)) %>%
dplyr::rename(name = source_name, type = source_type, subtype = source_subtype, gender = source_gender) %>%
dplyr::distinct()
G_book2 <- graph_from_data_frame(book2_edges, directed = FALSE, vertices = book2_nodes)
#print_all(G_book2)
G_book2## IGRAPH bb1f645 UNWB 16 21 --
## + attr: name (v/c), type (v/c), subtype (v/c), gender (v/c), volume
## | (v/c), title (v/c), publication_date (v/c), weight (e/n)
## + edges from bb1f645 (vertex names):
## [1] Frodo --Sam Gollum --Sam Frodo --Gollum Merry --Pippin
## [5] Gimli --Legolas Gandalf--Saruman Gandalf--Théoden Faramir--Frodo
## [9] Aragorn--Gandalf Aragorn--Legolas Aragorn--Gimli Gandalf--Treebeard
## [13] Merry --Treebeard Faramir--Sam Gandalf--Legolas Gandalf--Pippin
## [17] Pippin --Treebeard Gandalf--Gimli Aragorn--Éomer Boromir--Frodo
## [21] Gandalf--ShadowfaxCheck that the attributes were added to the nodes
vertex.attributes(G_book2)## $name
## [1] "Aragorn" "Boromir" "Éomer" "Faramir" "Frodo" "Gandalf"
## [7] "Gimli" "Gollum" "Legolas" "Merry" "Pippin" "Sam"
## [13] "Saruman" "Shadowfax" "Théoden" "Treebeard"
##
## $type
## [1] "per" "per" "per" "per" "per" "per" "per" "per" "per" "per" "per" "per"
## [13] "per" "per" "per" "per"
##
## $subtype
## [1] "men" "men" "men" "men" "hobbit" "ainur" "dwarf" "hobbit"
## [9] "elves" "hobbit" "hobbit" "hobbit" "ainur" "animal" "men" "ents"
##
## $gender
## [1] "male" "male" "male" "male" "male" "male" "male" "male" "male" "male"
## [11] "male" "male" "male" "male" "male" "male"
##
## $volume
## [1] "Book 2" "Book 2" "Book 2" "Book 2" "Book 2" "Book 2" "Book 2" "Book 2"
## [9] "Book 2" "Book 2" "Book 2" "Book 2" "Book 2" "Book 2" "Book 2" "Book 2"
##
## $title
## [1] "The Two Towers" "The Two Towers" "The Two Towers" "The Two Towers"
## [5] "The Two Towers" "The Two Towers" "The Two Towers" "The Two Towers"
## [9] "The Two Towers" "The Two Towers" "The Two Towers" "The Two Towers"
## [13] "The Two Towers" "The Two Towers" "The Two Towers" "The Two Towers"
##
## $publication_date
## [1] "1954-11-11" "1954-11-11" "1954-11-11" "1954-11-11" "1954-11-11"
## [6] "1954-11-11" "1954-11-11" "1954-11-11" "1954-11-11" "1954-11-11"
## [11] "1954-11-11" "1954-11-11" "1954-11-11" "1954-11-11" "1954-11-11"
## [16] "1954-11-11"Check that the undirected edges have weights
E(G_book2)## + 21/21 edges from bb1f645 (vertex names):
## [1] Frodo --Sam Gollum --Sam Frodo --Gollum Merry --Pippin
## [5] Gimli --Legolas Gandalf--Saruman Gandalf--Théoden Faramir--Frodo
## [9] Aragorn--Gandalf Aragorn--Legolas Aragorn--Gimli Gandalf--Treebeard
## [13] Merry --Treebeard Faramir--Sam Gandalf--Legolas Gandalf--Pippin
## [17] Pippin --Treebeard Gandalf--Gimli Aragorn--Éomer Boromir--Frodo
## [21] Gandalf--Shadowfaxedge.attributes(G_book2)## $weight
## [1] 158 101 99 51 50 49 46 41 38 34 28 26 25 24 23 23 23 22 21
## [20] 21 21Identify the largest connected component
book2_largest_cc <- clusters(G_book2)$membership == 1
G_book2_cc <- induced_subgraph(G_book2, book2_largest_cc)
G_book2_cc## IGRAPH 1059ae9 UNWB 11 15 --
## + attr: name (v/c), type (v/c), subtype (v/c), gender (v/c), volume
## | (v/c), title (v/c), publication_date (v/c), weight (e/n)
## + edges from 1059ae9 (vertex names):
## [1] Merry --Pippin Gimli --Legolas Gandalf--Saruman Gandalf--Théoden
## [5] Aragorn--Gandalf Aragorn--Legolas Aragorn--Gimli Gandalf--Treebeard
## [9] Merry --Treebeard Gandalf--Legolas Gandalf--Pippin Pippin --Treebeard
## [13] Gandalf--Gimli Aragorn--Éomer Gandalf--ShadowfaxAdd centrality measures to nodes in the largest connected component
V(G_book2_cc)$degree_centrality <- degree(G_book2_cc,
normalized = TRUE)
# weights = E(G_book2_cc, directed = FALSE)$weight,
V(G_book2_cc)$clustering_centrality <- transitivity(G_book2_cc,
type="local",
vids = NULL, # V(G_book1_cc),
weights = NA,
isolates = 'zero')
V(G_book2_cc)$closeness_centrality <- closeness(G_book2_cc,
weights = NA,
normalized = TRUE)
V(G_book2_cc)$betweenness_centrality <- betweenness(G_book2_cc,
directed = FALSE,
weights = NA,
normalized = TRUE)
V(G_book2_cc)$eigenvector_centrality <- eigen_centrality(G_book2_cc,
directed = FALSE,
weights = NA,
scale = FALSE)[["vector"]]
V(G_book2_cc)$pagerank_centrality <- page_rank(G_book2_cc,
algo = "prpack",
directed = FALSE,
damping = 0.9,
weights = NA)[["vector"]]
vertex.attributes(G_book2_cc)## $name
## [1] "Aragorn" "Éomer" "Gandalf" "Gimli" "Legolas" "Merry"
## [7] "Pippin" "Saruman" "Shadowfax" "Théoden" "Treebeard"
##
## $type
## [1] "per" "per" "per" "per" "per" "per" "per" "per" "per" "per" "per"
##
## $subtype
## [1] "men" "men" "ainur" "dwarf" "elves" "hobbit" "hobbit" "ainur"
## [9] "animal" "men" "ents"
##
## $gender
## [1] "male" "male" "male" "male" "male" "male" "male" "male" "male" "male"
## [11] "male"
##
## $volume
## [1] "Book 2" "Book 2" "Book 2" "Book 2" "Book 2" "Book 2" "Book 2" "Book 2"
## [9] "Book 2" "Book 2" "Book 2"
##
## $title
## [1] "The Two Towers" "The Two Towers" "The Two Towers" "The Two Towers"
## [5] "The Two Towers" "The Two Towers" "The Two Towers" "The Two Towers"
## [9] "The Two Towers" "The Two Towers" "The Two Towers"
##
## $publication_date
## [1] "1954-11-11" "1954-11-11" "1954-11-11" "1954-11-11" "1954-11-11"
## [6] "1954-11-11" "1954-11-11" "1954-11-11" "1954-11-11" "1954-11-11"
## [11] "1954-11-11"
##
## $degree_centrality
## [1] 0.4 0.1 0.8 0.3 0.3 0.2 0.3 0.1 0.1 0.1 0.3
##
## $clustering_centrality
## [1] 0.5000000 0.0000000 0.1428571 1.0000000 1.0000000 1.0000000 0.6666667
## [8] 0.0000000 0.0000000 0.0000000 0.6666667
##
## $closeness_centrality
## [1] 0.5882353 0.3846154 0.8333333 0.5555556 0.5555556 0.3846154 0.5555556
## [8] 0.4761905 0.4761905 0.4761905 0.5555556
##
## $betweenness_centrality
## [1] 0.20000000 0.00000000 0.80000000 0.00000000 0.00000000 0.00000000
## [7] 0.08888889 0.00000000 0.00000000 0.00000000 0.08888889
##
## $eigenvector_centrality
## [1] 0.3832493 0.1044969 0.5793725 0.3608614 0.3608614 0.1488724 0.2729997
## [8] 0.1579719 0.1579719 0.1579719 0.2729997
##
## $pagerank_centrality
## [1] 0.13076738 0.03851357 0.25847412 0.09655987 0.09655987 0.06805857
## [7] 0.09827943 0.03816925 0.03816925 0.03816925 0.09827943Convert G_book2 into JSON
G_book2_json <- d3r::d3_igraph(as.undirected(G_book2_cc))
G_book2_json## {"nodes":[{"name":"Aragorn","type":"per","subtype":"men","gender":"male","volume":"Book 2","title":"The Two Towers","publication_date":"1954-11-11","degree_centrality":0.4,"clustering_centrality":0.5,"closeness_centrality":0.5882,"betweenness_centrality":0.2,"eigenvector_centrality":0.3832,"pagerank_centrality":0.1308,"id":"Aragorn","_row":"Aragorn"},{"name":"Éomer","type":"per","subtype":"men","gender":"male","volume":"Book 2","title":"The Two Towers","publication_date":"1954-11-11","degree_centrality":0.1,"clustering_centrality":0,"closeness_centrality":0.3846,"betweenness_centrality":0,"eigenvector_centrality":0.1045,"pagerank_centrality":0.0385,"id":"Éomer","_row":"Éomer"},{"name":"Gandalf","type":"per","subtype":"ainur","gender":"male","volume":"Book 2","title":"The Two Towers","publication_date":"1954-11-11","degree_centrality":0.8,"clustering_centrality":0.1429,"closeness_centrality":0.8333,"betweenness_centrality":0.8,"eigenvector_centrality":0.5794,"pagerank_centrality":0.2585,"id":"Gandalf","_row":"Gandalf"},{"name":"Gimli","type":"per","subtype":"dwarf","gender":"male","volume":"Book 2","title":"The Two Towers","publication_date":"1954-11-11","degree_centrality":0.3,"clustering_centrality":1,"closeness_centrality":0.5556,"betweenness_centrality":0,"eigenvector_centrality":0.3609,"pagerank_centrality":0.0966,"id":"Gimli","_row":"Gimli"},{"name":"Legolas","type":"per","subtype":"elves","gender":"male","volume":"Book 2","title":"The Two Towers","publication_date":"1954-11-11","degree_centrality":0.3,"clustering_centrality":1,"closeness_centrality":0.5556,"betweenness_centrality":0,"eigenvector_centrality":0.3609,"pagerank_centrality":0.0966,"id":"Legolas","_row":"Legolas"},{"name":"Merry","type":"per","subtype":"hobbit","gender":"male","volume":"Book 2","title":"The Two Towers","publication_date":"1954-11-11","degree_centrality":0.2,"clustering_centrality":1,"closeness_centrality":0.3846,"betweenness_centrality":0,"eigenvector_centrality":0.1489,"pagerank_centrality":0.0681,"id":"Merry","_row":"Merry"},{"name":"Pippin","type":"per","subtype":"hobbit","gender":"male","volume":"Book 2","title":"The Two Towers","publication_date":"1954-11-11","degree_centrality":0.3,"clustering_centrality":0.6667,"closeness_centrality":0.5556,"betweenness_centrality":0.0889,"eigenvector_centrality":0.273,"pagerank_centrality":0.0983,"id":"Pippin","_row":"Pippin"},{"name":"Saruman","type":"per","subtype":"ainur","gender":"male","volume":"Book 2","title":"The Two Towers","publication_date":"1954-11-11","degree_centrality":0.1,"clustering_centrality":0,"closeness_centrality":0.4762,"betweenness_centrality":0,"eigenvector_centrality":0.158,"pagerank_centrality":0.0382,"id":"Saruman","_row":"Saruman"},{"name":"Shadowfax","type":"per","subtype":"animal","gender":"male","volume":"Book 2","title":"The Two Towers","publication_date":"1954-11-11","degree_centrality":0.1,"clustering_centrality":0,"closeness_centrality":0.4762,"betweenness_centrality":0,"eigenvector_centrality":0.158,"pagerank_centrality":0.0382,"id":"Shadowfax","_row":"Shadowfax"},{"name":"Théoden","type":"per","subtype":"men","gender":"male","volume":"Book 2","title":"The Two Towers","publication_date":"1954-11-11","degree_centrality":0.1,"clustering_centrality":0,"closeness_centrality":0.4762,"betweenness_centrality":0,"eigenvector_centrality":0.158,"pagerank_centrality":0.0382,"id":"Théoden","_row":"Théoden"},{"name":"Treebeard","type":"per","subtype":"ents","gender":"male","volume":"Book 2","title":"The Two Towers","publication_date":"1954-11-11","degree_centrality":0.3,"clustering_centrality":0.6667,"closeness_centrality":0.5556,"betweenness_centrality":0.0889,"eigenvector_centrality":0.273,"pagerank_centrality":0.0983,"id":"Treebeard","_row":"Treebeard"}],"links":[{"source":"Merry","target":"Pippin","weight":51},{"source":"Gimli","target":"Legolas","weight":50},{"source":"Gandalf","target":"Saruman","weight":49},{"source":"Gandalf","target":"Théoden","weight":46},{"source":"Aragorn","target":"Gandalf","weight":38},{"source":"Aragorn","target":"Legolas","weight":34},{"source":"Aragorn","target":"Gimli","weight":28},{"source":"Gandalf","target":"Treebeard","weight":26},{"source":"Merry","target":"Treebeard","weight":25},{"source":"Gandalf","target":"Legolas","weight":23},{"source":"Gandalf","target":"Pippin","weight":23},{"source":"Pippin","target":"Treebeard","weight":23},{"source":"Gandalf","target":"Gimli","weight":22},{"source":"Aragorn","target":"Éomer","weight":21},{"source":"Gandalf","target":"Shadowfax","weight":21}],"attributes":{}}# jsonlite::minify(G_book2_json)
# jsonlite::prettify(G_book2_json, indent = 4)Write G_book2 to JSON
write(G_book2_json, file = "data/LotR_Book2_from_R.json")Create a network graph for LotR Book 3
book3_df <- sqldf::sqldf("
SELECT
sour.id AS source_id, sour.label as source_name, sour.type AS source_type, sour.subtype AS source_subtype, sour.gender AS source_gender,
dest.id AS target_id, dest.label AS target_name, dest.type AS target_type, dest.subtype AS target_subtype, dest.gender AS target_gender,
conn.weight, conn.volume, conn.title, conn.publication_date
FROM
book3 conn
JOIN ontology sour
ON
conn.source = sour.id
JOIN ontology dest
ON
conn.target = dest.id
UNION
SELECT
dest.id AS source_id, dest.label as source_name, dest.type AS source_type, dest.subtype AS source_subtype, dest.gender AS source_gender,
sour.id AS target_id, sour.label AS target_name, sour.type AS target_type, sour.subtype AS target_subtype, sour.gender AS target_gender,
conn.weight, conn.volume, conn.title, conn.publication_date
FROM
book3 conn
JOIN ontology sour
ON
conn.source = sour.id
JOIN ontology dest
ON
conn.target = dest.id"
)
book3_df %>%
dplyr::mutate("weight" = as.double(weight),
"publication_date" = as.character(publication_date)) %>%
dplyr::arrange(desc(weight)) %>%
head(10)## source_id source_name source_type source_subtype source_gender target_id
## 1 frod Frodo per hobbit male sams
## 2 sams Sam per hobbit male frod
## 3 ganda Gandalf per ainur male pipp
## 4 pipp Pippin per hobbit male ganda
## 5 merr Merry per hobbit male pipp
## 6 pipp Pippin per hobbit male merr
## 7 arag Aragorn per men male ganda
## 8 dene Denethor per men male ganda
## 9 dene Denethor per men male pipp
## 10 ganda Gandalf per ainur male arag
## target_name target_type target_subtype target_gender weight volume
## 1 Sam per hobbit male 193 Book 3
## 2 Frodo per hobbit male 193 Book 3
## 3 Pippin per hobbit male 79 Book 3
## 4 Gandalf per ainur male 79 Book 3
## 5 Pippin per hobbit male 45 Book 3
## 6 Merry per hobbit male 45 Book 3
## 7 Gandalf per ainur male 34 Book 3
## 8 Gandalf per ainur male 34 Book 3
## 9 Pippin per hobbit male 34 Book 3
## 10 Aragorn per men male 34 Book 3
## title publication_date
## 1 The Return of the King 1955-10-20
## 2 The Return of the King 1955-10-20
## 3 The Return of the King 1955-10-20
## 4 The Return of the King 1955-10-20
## 5 The Return of the King 1955-10-20
## 6 The Return of the King 1955-10-20
## 7 The Return of the King 1955-10-20
## 8 The Return of the King 1955-10-20
## 9 The Return of the King 1955-10-20
## 10 The Return of the King 1955-10-20book3_edges <- sqldf::sqldf("
SELECT
sour.label as source_name, sour.type as source_type,
dest.label AS target_name, dest.type AS target_type,
conn.weight
FROM
book3 conn
JOIN ontology sour
ON
conn.source = sour.id
JOIN ontology dest
ON
conn.target = dest.id"
) %>%
dplyr::filter(source_type == "per", target_type == "per", weight > 20) %>%
dplyr::select(source_name, target_name, weight) %>%
dplyr::rename(from = source_name, to = target_name)
book3_nodes <- book3_df %>%
dplyr::filter(source_type == "per", target_type == "per", weight > 20) %>%
dplyr::select(source_name, source_type, source_subtype, source_gender, volume, title, publication_date) %>%
dplyr::mutate(publication_date = as.character(publication_date)) %>%
dplyr::rename(name = source_name, type = source_type, subtype = source_subtype, gender = source_gender) %>%
dplyr::distinct()
G_book3 <- graph_from_data_frame(book3_edges, directed = FALSE, vertices = book3_nodes)
#print_all(G_book3)
G_book3## IGRAPH b035c85 UNWB 13 19 --
## + attr: name (v/c), type (v/c), subtype (v/c), gender (v/c), volume
## | (v/c), title (v/c), publication_date (v/c), weight (e/n)
## + edges from b035c85 (vertex names):
## [1] Frodo --Sam Gandalf --Pippin Merry --Pippin Aragorn --Gandalf
## [5] Denethor--Gandalf Denethor--Pippin Gimli --Legolas Aragorn --Gimli
## [9] Beregond--Pippin Frodo --Pippin Aragorn --Legolas Aragorn --Éomer
## [13] Faramir --Gandalf Faramir --Pippin Frodo --Gandalf Aragorn --Merry
## [17] Denethor--Faramir Éowyn --Merry Pippin --SamCheck that the attributes were added to the nodes
vertex.attributes(G_book3)## $name
## [1] "Aragorn" "Beregond" "Denethor" "Éomer" "Éowyn" "Faramir"
## [7] "Frodo" "Gandalf" "Gimli" "Legolas" "Merry" "Pippin"
## [13] "Sam"
##
## $type
## [1] "per" "per" "per" "per" "per" "per" "per" "per" "per" "per" "per" "per"
## [13] "per"
##
## $subtype
## [1] "men" "men" "men" "men" "men" "men" "hobbit" "ainur"
## [9] "dwarf" "elves" "hobbit" "hobbit" "hobbit"
##
## $gender
## [1] "male" "male" "male" "male" "female" "male" "male" "male"
## [9] "male" "male" "male" "male" "male"
##
## $volume
## [1] "Book 3" "Book 3" "Book 3" "Book 3" "Book 3" "Book 3" "Book 3" "Book 3"
## [9] "Book 3" "Book 3" "Book 3" "Book 3" "Book 3"
##
## $title
## [1] "The Return of the King" "The Return of the King" "The Return of the King"
## [4] "The Return of the King" "The Return of the King" "The Return of the King"
## [7] "The Return of the King" "The Return of the King" "The Return of the King"
## [10] "The Return of the King" "The Return of the King" "The Return of the King"
## [13] "The Return of the King"
##
## $publication_date
## [1] "1955-10-20" "1955-10-20" "1955-10-20" "1955-10-20" "1955-10-20"
## [6] "1955-10-20" "1955-10-20" "1955-10-20" "1955-10-20" "1955-10-20"
## [11] "1955-10-20" "1955-10-20" "1955-10-20"Check that the undirected edges have weights
E(G_book3)## + 19/19 edges from b035c85 (vertex names):
## [1] Frodo --Sam Gandalf --Pippin Merry --Pippin Aragorn --Gandalf
## [5] Denethor--Gandalf Denethor--Pippin Gimli --Legolas Aragorn --Gimli
## [9] Beregond--Pippin Frodo --Pippin Aragorn --Legolas Aragorn --Éomer
## [13] Faramir --Gandalf Faramir --Pippin Frodo --Gandalf Aragorn --Merry
## [17] Denethor--Faramir Éowyn --Merry Pippin --Samedge.attributes(G_book3)## $weight
## [1] 193 79 45 34 34 34 32 28 27 27 26 24 24 24 24 21 21 21 21Identify the largest connected component
book3_largest_cc <- clusters(G_book3)$membership == 1
G_book3_cc <- induced_subgraph(G_book3, book3_largest_cc)
G_book3_cc## IGRAPH 5f72b48 UNWB 13 19 --
## + attr: name (v/c), type (v/c), subtype (v/c), gender (v/c), volume
## | (v/c), title (v/c), publication_date (v/c), weight (e/n)
## + edges from 5f72b48 (vertex names):
## [1] Frodo --Sam Gandalf --Pippin Merry --Pippin Aragorn --Gandalf
## [5] Denethor--Gandalf Denethor--Pippin Gimli --Legolas Aragorn --Gimli
## [9] Beregond--Pippin Frodo --Pippin Aragorn --Legolas Aragorn --Éomer
## [13] Faramir --Gandalf Faramir --Pippin Frodo --Gandalf Aragorn --Merry
## [17] Denethor--Faramir Éowyn --Merry Pippin --SamAdd centrality measures to nodes in the largest connected component
V(G_book3_cc)$degree_centrality <- degree(G_book3_cc,
normalized = TRUE)
# weights = E(G_book3_cc, directed = FALSE)$weight,
V(G_book3_cc)$clustering_centrality <- transitivity(G_book3_cc,
type="local",
vids = NULL, # V(G_book1_cc),
weights = NA,
isolates = 'zero')
V(G_book3_cc)$closeness_centrality <- closeness(G_book3_cc,
weights = NA,
normalized = TRUE)
V(G_book3_cc)$betweenness_centrality <- betweenness(G_book3_cc,
directed = FALSE,
weights = NA,
normalized = TRUE)
V(G_book3_cc)$eigenvector_centrality <- eigen_centrality(G_book3_cc,
directed = FALSE,
weights = NA,
scale = FALSE)[["vector"]]
V(G_book3_cc)$pagerank_centrality <- page_rank(G_book3_cc,
algo = "prpack",
directed = FALSE,
damping = 0.9,
weights = NA)[["vector"]]
vertex.attributes(G_book3_cc)## $name
## [1] "Aragorn" "Beregond" "Denethor" "Éomer" "Éowyn" "Faramir"
## [7] "Frodo" "Gandalf" "Gimli" "Legolas" "Merry" "Pippin"
## [13] "Sam"
##
## $type
## [1] "per" "per" "per" "per" "per" "per" "per" "per" "per" "per" "per" "per"
## [13] "per"
##
## $subtype
## [1] "men" "men" "men" "men" "men" "men" "hobbit" "ainur"
## [9] "dwarf" "elves" "hobbit" "hobbit" "hobbit"
##
## $gender
## [1] "male" "male" "male" "male" "female" "male" "male" "male"
## [9] "male" "male" "male" "male" "male"
##
## $volume
## [1] "Book 3" "Book 3" "Book 3" "Book 3" "Book 3" "Book 3" "Book 3" "Book 3"
## [9] "Book 3" "Book 3" "Book 3" "Book 3" "Book 3"
##
## $title
## [1] "The Return of the King" "The Return of the King" "The Return of the King"
## [4] "The Return of the King" "The Return of the King" "The Return of the King"
## [7] "The Return of the King" "The Return of the King" "The Return of the King"
## [10] "The Return of the King" "The Return of the King" "The Return of the King"
## [13] "The Return of the King"
##
## $publication_date
## [1] "1955-10-20" "1955-10-20" "1955-10-20" "1955-10-20" "1955-10-20"
## [6] "1955-10-20" "1955-10-20" "1955-10-20" "1955-10-20" "1955-10-20"
## [11] "1955-10-20" "1955-10-20" "1955-10-20"
##
## $degree_centrality
## [1] 0.41666667 0.08333333 0.25000000 0.08333333 0.08333333 0.25000000
## [7] 0.25000000 0.41666667 0.16666667 0.16666667 0.25000000 0.58333333
## [13] 0.16666667
##
## $clustering_centrality
## [1] 0.1000000 0.0000000 1.0000000 0.0000000 0.0000000 1.0000000 0.6666667
## [8] 0.4000000 1.0000000 1.0000000 0.0000000 0.2380952 1.0000000
##
## $closeness_centrality
## [1] 0.5714286 0.3870968 0.4800000 0.3750000 0.3750000 0.4800000 0.4800000
## [8] 0.6000000 0.3870968 0.3870968 0.5714286 0.6000000 0.4000000
##
## $betweenness_centrality
## [1] 0.45454545 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
## [7] 0.02777778 0.29797980 0.00000000 0.00000000 0.24747475 0.39646465
## [13] 0.00000000
##
## $eigenvector_centrality
## [1] 0.23082225 0.13631009 0.34419409 0.05996801 0.05468441 0.34419409
## [7] 0.31118983 0.45597013 0.08101613 0.08101613 0.21048519 0.52466977
## [13] 0.21715772
##
## $pagerank_centrality
## [1] 0.13646966 0.02976743 0.07365198 0.03225685 0.03286561 0.07365198
## [7] 0.07508870 0.12104976 0.05864881 0.05864881 0.08391102 0.17169536
## [13] 0.05229404Convert G_book3 into JSON
G_book3_json <- d3r::d3_igraph(as.undirected(G_book3_cc))
G_book3_json## {"nodes":[{"name":"Aragorn","type":"per","subtype":"men","gender":"male","volume":"Book 3","title":"The Return of the King","publication_date":"1955-10-20","degree_centrality":0.4167,"clustering_centrality":0.1,"closeness_centrality":0.5714,"betweenness_centrality":0.4545,"eigenvector_centrality":0.2308,"pagerank_centrality":0.1365,"id":"Aragorn","_row":"Aragorn"},{"name":"Beregond","type":"per","subtype":"men","gender":"male","volume":"Book 3","title":"The Return of the King","publication_date":"1955-10-20","degree_centrality":0.0833,"clustering_centrality":0,"closeness_centrality":0.3871,"betweenness_centrality":0,"eigenvector_centrality":0.1363,"pagerank_centrality":0.0298,"id":"Beregond","_row":"Beregond"},{"name":"Denethor","type":"per","subtype":"men","gender":"male","volume":"Book 3","title":"The Return of the King","publication_date":"1955-10-20","degree_centrality":0.25,"clustering_centrality":1,"closeness_centrality":0.48,"betweenness_centrality":0,"eigenvector_centrality":0.3442,"pagerank_centrality":0.0737,"id":"Denethor","_row":"Denethor"},{"name":"Éomer","type":"per","subtype":"men","gender":"male","volume":"Book 3","title":"The Return of the King","publication_date":"1955-10-20","degree_centrality":0.0833,"clustering_centrality":0,"closeness_centrality":0.375,"betweenness_centrality":0,"eigenvector_centrality":0.06,"pagerank_centrality":0.0323,"id":"Éomer","_row":"Éomer"},{"name":"Éowyn","type":"per","subtype":"men","gender":"female","volume":"Book 3","title":"The Return of the King","publication_date":"1955-10-20","degree_centrality":0.0833,"clustering_centrality":0,"closeness_centrality":0.375,"betweenness_centrality":0,"eigenvector_centrality":0.0547,"pagerank_centrality":0.0329,"id":"Éowyn","_row":"Éowyn"},{"name":"Faramir","type":"per","subtype":"men","gender":"male","volume":"Book 3","title":"The Return of the King","publication_date":"1955-10-20","degree_centrality":0.25,"clustering_centrality":1,"closeness_centrality":0.48,"betweenness_centrality":0,"eigenvector_centrality":0.3442,"pagerank_centrality":0.0737,"id":"Faramir","_row":"Faramir"},{"name":"Frodo","type":"per","subtype":"hobbit","gender":"male","volume":"Book 3","title":"The Return of the King","publication_date":"1955-10-20","degree_centrality":0.25,"clustering_centrality":0.6667,"closeness_centrality":0.48,"betweenness_centrality":0.0278,"eigenvector_centrality":0.3112,"pagerank_centrality":0.0751,"id":"Frodo","_row":"Frodo"},{"name":"Gandalf","type":"per","subtype":"ainur","gender":"male","volume":"Book 3","title":"The Return of the King","publication_date":"1955-10-20","degree_centrality":0.4167,"clustering_centrality":0.4,"closeness_centrality":0.6,"betweenness_centrality":0.298,"eigenvector_centrality":0.456,"pagerank_centrality":0.121,"id":"Gandalf","_row":"Gandalf"},{"name":"Gimli","type":"per","subtype":"dwarf","gender":"male","volume":"Book 3","title":"The Return of the King","publication_date":"1955-10-20","degree_centrality":0.1667,"clustering_centrality":1,"closeness_centrality":0.3871,"betweenness_centrality":0,"eigenvector_centrality":0.081,"pagerank_centrality":0.0586,"id":"Gimli","_row":"Gimli"},{"name":"Legolas","type":"per","subtype":"elves","gender":"male","volume":"Book 3","title":"The Return of the King","publication_date":"1955-10-20","degree_centrality":0.1667,"clustering_centrality":1,"closeness_centrality":0.3871,"betweenness_centrality":0,"eigenvector_centrality":0.081,"pagerank_centrality":0.0586,"id":"Legolas","_row":"Legolas"},{"name":"Merry","type":"per","subtype":"hobbit","gender":"male","volume":"Book 3","title":"The Return of the King","publication_date":"1955-10-20","degree_centrality":0.25,"clustering_centrality":0,"closeness_centrality":0.5714,"betweenness_centrality":0.2475,"eigenvector_centrality":0.2105,"pagerank_centrality":0.0839,"id":"Merry","_row":"Merry"},{"name":"Pippin","type":"per","subtype":"hobbit","gender":"male","volume":"Book 3","title":"The Return of the King","publication_date":"1955-10-20","degree_centrality":0.5833,"clustering_centrality":0.2381,"closeness_centrality":0.6,"betweenness_centrality":0.3965,"eigenvector_centrality":0.5247,"pagerank_centrality":0.1717,"id":"Pippin","_row":"Pippin"},{"name":"Sam","type":"per","subtype":"hobbit","gender":"male","volume":"Book 3","title":"The Return of the King","publication_date":"1955-10-20","degree_centrality":0.1667,"clustering_centrality":1,"closeness_centrality":0.4,"betweenness_centrality":0,"eigenvector_centrality":0.2172,"pagerank_centrality":0.0523,"id":"Sam","_row":"Sam"}],"links":[{"source":"Frodo","target":"Sam","weight":193},{"source":"Gandalf","target":"Pippin","weight":79},{"source":"Merry","target":"Pippin","weight":45},{"source":"Aragorn","target":"Gandalf","weight":34},{"source":"Denethor","target":"Gandalf","weight":34},{"source":"Denethor","target":"Pippin","weight":34},{"source":"Gimli","target":"Legolas","weight":32},{"source":"Aragorn","target":"Gimli","weight":28},{"source":"Beregond","target":"Pippin","weight":27},{"source":"Frodo","target":"Pippin","weight":27},{"source":"Aragorn","target":"Legolas","weight":26},{"source":"Aragorn","target":"Éomer","weight":24},{"source":"Faramir","target":"Gandalf","weight":24},{"source":"Faramir","target":"Pippin","weight":24},{"source":"Frodo","target":"Gandalf","weight":24},{"source":"Aragorn","target":"Merry","weight":21},{"source":"Denethor","target":"Faramir","weight":21},{"source":"Éowyn","target":"Merry","weight":21},{"source":"Pippin","target":"Sam","weight":21}],"attributes":{}}# jsonlite::minify(G_book3_json)
# jsonlite::prettify(G_book3_json, indent = 4)Write G_book3 to JSON
write(G_book3_json, file = "data/LotR_Book3_from_R.json")References
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