##           group 1         group 2         group 3        group 4
## 1 Batson, Anthony    Mendoza, Ava   Pacheco, Alex           <NA>
## 2    Myoung, Sein Randall, Javion Bell, Mary Rose    Ong, Alyssa
## 3     Qin, Celine Kang, Christine     Smith, Reid    Pham, Canon
## 4                   Leahy, Olivia  Knowles, Genny Devir, Lindsey
##             group 5
## 1 Wolfenstein, Luci
## 2 Mahoney, Brigette
## 3      Barga, Jolie
## 4     Moore, Allana

• Create a visualization with the provided network data

##           group 1         group 2         group 3        group 4
## 1 Batson, Anthony    Mendoza, Ava   Pacheco, Alex           <NA>
## 2    Myoung, Sein Randall, Javion Bell, Mary Rose    Ong, Alyssa
## 3     Qin, Celine Kang, Christine     Smith, Reid    Pham, Canon
## 4                   Leahy, Olivia  Knowles, Genny Devir, Lindsey
##             group 5
## 1 Wolfenstein, Luci
## 2 Mahoney, Brigette
## 3      Barga, Jolie
## 4     Moore, Allana

• Create a visualization with the provided network data
• How did you represent the data?
• What are the important components?
• What message do you seek to communicate?
• What challenges/questions came up?

• On Wednesday, we will plot networks!

• Warm-up: network data
• What is network data?
• Network metrics
• Activity: Calculating networks by hand
• Mid-quarter evaluation

• Introduction to igraph
• Network centrality with authorship data
• Network data and tidycensus

• Office Hours:Friday 1:30-3:30pm (Tyler)
• Tuesdays, 10:30am-12:00pm (Yao)

• Final Project: Collaboration encouraged, track individual contributions (e.g. through GitHub)
• Final Project Rubric: Will be available this week
• May 13th: Guest speaker from Recidiviz

• Community Mapping Prejudice Session: Transform Historic Racial Covenants into Actionable Data
• How does this relate to prior lessons?
• Mapping Racial Covenants
• Example Map
• The Zooniverse

• Motivate examination of network data
• Understand network structure (node vs. edge, directed vs. undirected)
• Understand different types of centrality and what these mean
• (Wednesday) Learn how to plot networks using igraph

• Up to this point, our units of analysis have mostly been people and places
• What if we want to study connections between people or places?

• Activity Spaces
• Friendship ties
• Funding connections
• Migration flows

• Two elements:

1. Nodes
2. Edges

Network example. From Nykamp DQ, An introduction to networks.

• Two types of edges:

1. Directed

• e.g. cash payments, job applications, academic citations, etc.

1. Undirected

Directed Network. From [Nykamp DQ, An introduction to networks.

• Two types of edges:

1. Directed
2. Undirected

• e.g. friendship ties, common board members, shared destinations, etc.

Undirected Network. From Nykamp DQ, An introduction to networks.

• In groups:
• In the warm up, what are the nodes? edges?
• Is the data undirected or directed?
• We can modify the nodes and edges according to various characteristics to make our visuals more interesting

• Nodes are users
• Edges are twitter interactions
• Colors based on opinions

• Nodes are actors
• Edges are information shared
• Color based on agreement with ‘There should be an international binding commitment on all nations to reduce GHG emissions’.

• One-mode vs. Two-mode

• Some networks have multiple “modes” or levels
• For example, two-mode network below
• Small nodes are actors, large nodes are organizations:

• Can represent this as one-mode network
• Now ties represent shared actors
• Colors represent funding from Koch/Exxon (green) or not (red)

• In pairs:
• How would you describe the following network? (one mode, two mode)
• Could it be projected to a one-mode network? How?

• Nodes and edges are the building blocks of networks
• Networks can be directed or undirected
• Two mode networks have two levels (e.g. individuals, institutions)

• We might want to evaluate the central nodes in our network
• For example: centrality in a network might represent social capital or influence

• Degree Centrality
• Node with the highest number of ties is most central
• Think: most friends

• Betweenness Centrality
• Based on “shortest paths” between nodes, node involved in most “shortest paths” is most central
• Think: who is involved in the most friendship pathways?

• Closeness Centrality
• Based on “shortest paths” between nodes, node with lowest average “shortest path” to the others is most central
• Think: who could spread a message fastest?

• Eigenvalue Centrality
• Based on the degree of adjacent nodes, node with “friends in high places” is most central
• Think: who has friends with the most connections?

• Group activity:
• Which point(s) have the highest degree centrality? (most edges)
• Betweenness centrality? (involved in most “shortest paths”)
• Closeness centrality? (lowest average “shortest path” to others)
• Eigenvalue Centrality? (“friends in high places”)

• Centrality is a way to measure the imporance of a network position
• There are many different measures of centrality
• We can choose a measure based on our theory of why centrality is important (e.g. number of edges, betweenness, closeness, friends in high places)

• Create a visualization with the provided network data
• Consider using color/scale/labels/comparisons
• In your visualization, which are most central nodes?

##           group 1         group 2         group 3        group 4
## 1 Batson, Anthony    Mendoza, Ava   Pacheco, Alex           <NA>
## 2    Myoung, Sein Randall, Javion Bell, Mary Rose    Ong, Alyssa
## 3     Qin, Celine Kang, Christine     Smith, Reid    Pham, Canon
## 4                   Leahy, Olivia  Knowles, Genny Devir, Lindsey
##             group 5
## 1 Wolfenstein, Luci
## 2 Mahoney, Brigette
## 3      Barga, Jolie
## 4     Moore, Allana

• Introduction to igraph
• Network visualization and centrality with authorship data

• Office Hours:Friday 1:30-3:30pm (Tyler)
• Tuesdays, 10:30am-12:00pm (Yao)

• PSets due on Tuesdays! Starting with PSet 6
• Final Project Rubric available on Canvas
• May 13th: Guest speaker from Recidiviz

• Build our own networks in R
• Calculate centrality measures
• Set network characteristics

• Let’s create a network!
• We’ll represent friendship ties among 7 people
• We’ll call it el for “edge list”
• Notice how the data structure is different
• Needs to be a matrix

el <- data.frame(person_1 = c("Lionel", "Frederica", "Garrett", "Lina",
                               "Sampson", "Garrett", "Frederica", "Lionel",
                              "Frederica", "Frederica", "Ahmad"),
                  person_2 = c("Lina", "Charlotte", "Lina", "Sampson",
                               "Charlotte", "Lionel", "Lina", "Sampson",
                               "Sampson", "Garrett", "Garrett")) %>%
  as.matrix()
# take a look
el

##       person_1    person_2   
##  [1,] "Lionel"    "Lina"     
##  [2,] "Frederica" "Charlotte"
##  [3,] "Garrett"   "Lina"     
##  [4,] "Lina"      "Sampson"  
##  [5,] "Sampson"   "Charlotte"
##  [6,] "Garrett"   "Lionel"   
##  [7,] "Frederica" "Lina"     
##  [8,] "Lionel"    "Sampson"  
##  [9,] "Frederica" "Sampson"  
## [10,] "Frederica" "Garrett"  
## [11,] "Ahmad"     "Garrett"

• Create your own:

el <- data.frame(person_1 = c("Lionel", "Frederica", "Garrett", "Lina",
                               "Sampson", "Garrett", "Frederica", "Lionel",
                              "Frederica", "Frederica", "Ahmad"),
                  person_2 = c("Lina", "Charlotte", "Lina", "Sampson",
                               "Charlotte", "Lionel", "Lina", "Sampson",
                               "Sampson", "Garrett", "Garrett")) %>%
  as.matrix()
# take a look
el

##       person_1    person_2   
##  [1,] "Lionel"    "Lina"     
##  [2,] "Frederica" "Charlotte"
##  [3,] "Garrett"   "Lina"     
##  [4,] "Lina"      "Sampson"  
##  [5,] "Sampson"   "Charlotte"
##  [6,] "Garrett"   "Lionel"   
##  [7,] "Frederica" "Lina"     
##  [8,] "Lionel"    "Sampson"  
##  [9,] "Frederica" "Sampson"  
## [10,] "Frederica" "Garrett"  
## [11,] "Ahmad"     "Garrett"

• We can use igraph to create a network object
• Should it be directed?

library(igraph)

# create network from edge list
net <- graph_from_edgelist(el)

• Let’s assume friendships are bidirectional (undirected)

library(igraph)

# create network from edge list
net <- graph_from_edgelist(el, directed = FALSE)

• Let’s try plotting our network!

# plot network
plot(net)

• We can adjust the graph using arguments that start with vertex and edge

# customize network plot
plot(net, vertex.size = 30, 
     vertex.color = "lavender", 
     vertex.frame.color = NA, 
     vertex.label.cex = .7, 
     edge.curved = .05, 
     edge.arrow.size = .3, 
     edge.width = .7, 
     edge.color = "gray1")

• We can adjust the graph using arguments that start with vertex and edge

# customize network plot
plot(net, vertex.size = 30, 
     vertex.color = "lavender", 
     vertex.frame.color = NA, 
     vertex.label.cex = .7, 
     edge.curved = .05, 
     edge.arrow.size = .3, 
     edge.width = .7, 
     edge.color = "gray1")

• Degree Centrality
• Based on number of edges, node with most edges is most central
• degree()

• Betweenness Centrality
• Based on “shortest paths” between nodes, node involved in most “shortest paths” is most central
• betweenness()

• Closeness Centrality
• Based on “shortest paths” between nodes, node with lowest average “shortest path” to the others is most central
• closeness()

• Eigenvalue Centrality
• Based on the degree of adjacent nodes, node with “friends in high places” is most central
• evcent()

• With el, calculate centrality!
• Use degree, betweenness, closeness, and evcent
• Which has the highest closeness score?
• Which has the highest eigenvalue centrality score?

el <- data.frame(person_1 = c("Lionel", "Frederica", "Garrett", "Lina",
                               "Sampson", "Garrett", "Frederica", "Lionel",
                              "Frederica", "Frederica", "Ahmad"),
                  person_2 = c("Lina", "Charlotte", "Lina", "Sampson",
                               "Charlotte", "Lionel", "Lina", "Sampson",
                               "Sampson", "Garrett", "Garrett")) %>%
  as.matrix()
# take a look
el

##       person_1    person_2   
##  [1,] "Lionel"    "Lina"     
##  [2,] "Frederica" "Charlotte"
##  [3,] "Garrett"   "Lina"     
##  [4,] "Lina"      "Sampson"  
##  [5,] "Sampson"   "Charlotte"
##  [6,] "Garrett"   "Lionel"   
##  [7,] "Frederica" "Lina"     
##  [8,] "Lionel"    "Sampson"  
##  [9,] "Frederica" "Sampson"  
## [10,] "Frederica" "Garrett"  
## [11,] "Ahmad"     "Garrett"

# create network from edge list
net <- graph_from_edgelist(el, directed = FALSE)

• How would we normally create a variable?
• mutate()
• Does this work with a network?
• Try net %>% mutate()

• Network data are not like other data we’ve worked with
• Is net a dataframe? How would we find out?
• class(net)

• We can explore network characteristics with V()
• Try it! V(net)
• We can call variables with the $ sign (similar to dataframes)
• We can set variables using V(net)$variable <- newvariable
• Let’s try it!

V(net)$betweenness <- betweenness(net)

• Try setting betweenness, closeness, degree, eigenvalue centrality

V(net)$betweenness <- betweenness(net)

• A benefit of setting characteristics: we can plot with them!
• Try modifying vertex.size = V(net)$betweenness
• Try modifying other characteristics too

plot(net, 
     vertex.size = V(net)$betweenness*10, 
     vertex.color = "lavender", 
     vertex.frame.color = NA, 
     vertex.label.cex = .5, 
     edge.curved = .05, 
     edge.width = .1, 
     edge.color = "gray1")

• IPCC has written 6 climate assessments since 1990 (FAR - AR6)
• Three working groups:
• WGI: physical and scientific basis of climate change
• WGII: vulnerability of natural and social systems to climate change
• WGIII: mitigation strategies and policy recommendations
• All of these influence global policies and mitigation strategies
• Geographic bias? Most authors come from “Global North” countries

• Let’s take a look at the WGIII authors
• Try the following code (section 6.4 of course site)
• Then examine your data with View()
• How would you describe your data?

library(RCurl)

# input url from github
url <- getURL("https://raw.githubusercontent.com/tylermcdaniel/css/main/Data/IPCC_co_authorship.csv")

# download authorship data (from github)
ipcc_authors <- read_csv(url, skip = 1)

# replace NA's with 0's
ipcc_authors %<>%
  mutate_all(~replace(., is.na(.), 0))

• Need to clean up data

library(dplyr)
# reorder column names to match rows
ipcc_authors %<>%
  select(order(colnames(.)))


# turn dataframe into matrix
ipcc_authors %<>%
  select(-Author) %>%
  as.matrix()

• Now we can turn it into a network!

ipcc_net <- graph_from_adjacency_matrix(ipcc_authors,
                                        mode = "undirected")

• Try it on your own!

# reorder column names to match rows
ipcc_authors %<>%
  select(order(colnames(.)))


# turn dataframe into matrix
ipcc_authors %<>%
  select(-Author) %>%
  as.matrix()

ipcc_net <- graph_from_adjacency_matrix(ipcc_authors,
                                        mode = "undirected")

• Try plotting

plot(ipcc_net, vertex.size = 2, 
     vertex.color = "lavender", 
     vertex.frame.color = NA, 
     vertex.label.cex = .5, 
     edge.curved = .05, 
     edge.width = .1, 
     edge.color = "gray1")

• Let’s only look at \(\ge2\) collaborations

# replace 1s with 0s
ipcc_authors[ipcc_authors == 1] = 0

# replace NAs with 0s
ipcc_authors[is.na(ipcc_authors)] = 0

• Let’s remove authors who did not collaborate with anyone

# vector of authors who do not collaborate with others
no_colab <- which(apply(ipcc_authors, 1, sum, na.rm = TRUE) == 0)


# then we can remove these from ipcc_authors
ipcc_authors <- ipcc_authors[-no_colab,
                             -no_colab]

• Now let’s try again

# create network, again
ipcc_net <- graph_from_adjacency_matrix(ipcc_authors,
                                        mode = "undirected")

plot(ipcc_net, vertex.size = 2, 
     vertex.color = "lavender", 
     vertex.frame.color = NA, 
     vertex.label.cex = .5, 
     edge.curved = .05, 
     edge.width = .1, 
     edge.color = "gray1")

• We can set network characteristics using V()

# add betweenness centrality
V(ipcc_net)$betweenness <- betweenness(ipcc_net)

• We can use network characteristics to format plot

plot(ipcc_net, 
     vertex.size = V(ipcc_net)$betweenness/max(V(ipcc_net)$betweenness) * 20, 
     vertex.color = "lavender", 
     vertex.frame.color = NA, 
     vertex.label.cex = .5, 
     edge.curved = .05, 
     edge.width = .1, 
     edge.color = "gray1")

• Create new igraph object
• Can change weighted = TRUE to weight by collaborations

# create network, again
ipcc_net <- graph_from_adjacency_matrix(ipcc_authors,
                                        mode = "undirected",
                                        weighted = TRUE)

• We set network characteristics using V()

# add betweenness centrality
V(ipcc_net)$betweenness <- betweenness(ipcc_net)

• We can examine the “most central” authors, according to betweeenness scores

# show authors in descending order
V(ipcc_net)[order(V(ipcc_net)$betweenness, decreasing = TRUE)]

## + 148/148 vertices, named, from 23c573d:
##   [1] Shukla             Schaeffer          Smith             
##   [4] Edenhofer          Price              Carraro           
##   [7] Uerge-Vorsatz      Krey               Riahi             
##  [10] Clarke             Rogner             Lutz              
##  [13] Kahn-Ribeiro       Nakicenovic        Winkler           
##  [16] Hoehne             Paltsev            Michaelowa        
##  [19] Strachan           Sathaye            Faaij             
##  [22] Hourcade           Ravindranath       Halsnaes          
##  [25] Bosetti            Zhang              Skea              
##  [28] Den-Elzen          Lecocq             Fischedick        
## + ... omitted several vertices

• We can specify that we want edge width to be proportional to weights:

# plot network
plot(ipcc_net, 
   edge.width=(E(ipcc_net)$weight)/5,
    vertex.size = V(ipcc_net)$betweenness/max(V(ipcc_net)$betweenness) * 20, 
     vertex.color = "lavender", 
     vertex.alpha = 0.5,
     vertex.frame.color = NA, 
     vertex.label.cex = .5, 
     edge.curved = .05, 
     edge.width = .1, 
     edge.color = "gray1")

• We can specify that we want edge width to be proportional to weights:

• What else could we add to the plot?

• We could add region to examine differences in network centrality

# input url from github
url <- getURL("https://raw.githubusercontent.com/tylermcdaniel/css/main/Data/IPCC_cv.csv")

# download authorship data (from github)
ipcc_cvs <- read_csv(url)

# remove authors who did not collaborate
ipcc_cvs %<>%
  slice(-no_colab)

• We could add region to examine differences in network centrality

# define global regions
ipcc_cvs %<>%
  mutate(region = case_match(`IPCC representing country (i.e. Country of residence from IPCC doc)`,
                             # Europe will be green
                             c("Austria", "Belgium", "Denmark", "Finland", 
                               "France", "Germany", "Greece", "Hungary", "Italy",
                               "Netherlands", "Norway", "Spain", "Sweden", 
                               "Switzerland", "UK") ~ "green4", 
                             # North America will be red
                             c("Canada", "USA", "Mexico") ~ "tomato",
                             # BRICS will be blue
                             c("Brazil", "Russia", "India", "China", 
                               "South Africa") ~ "steelblue", 
                             # Other countries will be gold
                             .default = "gold"))

• Define region variable for the vertices

# define country variable
V(ipcc_net)$region <- ipcc_cvs$region

• Can change vertex color using vertex.color

# plot network
plot(ipcc_net, 
   edge.width=(E(ipcc_net)$weight)/5,
    vertex.size = V(ipcc_net)$betweenness/max(V(ipcc_net)$betweenness) * 20, 
     vertex.color = V(ipcc_net)$region, 
     vertex.alpha = 0.5,
     vertex.frame.color = NA, 
     vertex.label.cex = .5, 
     edge.curved = .05, 
     edge.width = .1, 
     edge.color = "gray1")

• Finally, we can add a legend manually

# add legend
legend(
  "bottomright",
  legend = c("Europe", "North America", "BRICS", "Other"),
  pt.bg  = c("green4", "tomato", "steelblue", "gold"),
  pch    = 21,
  cex    = 1,
  title  = "Region"
  )

• Finally, we can add a legend manually

• First, transform igraph object to networkd3 object

library(networkD3)

# create dataframe for networkD3
ipcc_d3 <- igraph_to_networkD3(ipcc_net, group = V(ipcc_net)$region)

• Next, set color palette (optional)

# set color scale
ColourScale <- 'd3.scaleOrdinal()
            .domain(["Europe", "North America", "BRICS", "Other"])
           .range(["#07C343", "#D2140C", "#0C4AD2", "#C7D20C"]);'

• Then use forceNetwork() to build interactive network

p <- forceNetwork(Links = ipcc_d3$links,
                  Nodes = ipcc_d3$nodes,
                  Group = "group",
                  height="400px", width="800px",
                  NodeID = "name",
                  fontSize = 14,
                  colourScale = JS(ColourScale),
                  zoom = TRUE)

• Plot network!

# plot network!
p

• PSets due on Tuesdays! Starting with PSet 6
• Final Project Rubric available on Canvas
• May 13th: Guest speaker from Recidiviz