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This R markdown script will help you analyze and visualize the social networks (Trust, Advice, and Communication) for you MBA class.
In the class networks (communication, trust, and advice) what are your centrality measures and how do they compare to those of your classmates (i.e., where are you in the distribution?). Please refer both from both tables and network graph.
#Install the following packages prior to running the code
library(igraph)
library(dplyr)
library(readxl)
library(qgraph)
library(tidyverse)
library(knitr)
library(DT)
library(readr)
library(visNetwork)
# Loading and inspecting data
# Set your own working directory to where you saved the class files. You will have to uncomment out the next line.
#path<-"//Users/brandyaven/Library/CloudStorage/GoogleDrive-aven@andrew.cmu.edu/My Drive/Teaching/1_MON_Macro Core/0_MASTERFILES/Head TA Share/2023 PTOH Class Data/"
path<-"/Users/chaoyiz/Desktop/CMU/MBA/MBA_Networks/2024"
setwd(path)
network_data<- load("2024Jul31-2024_M6_PTOH_All-Graphs.RData")
# File upload codeNetwork Size refers to the number of nodes in the
network.
## The network size of trust graph is 105## The network size of commnuication graph is 105## The network size of advice graph is 105Density refers to proportion of possible ties that
actually realized in the network. It is calculated by dividing the
number of observed connections in the network by the total number of
possible connections. A high edge density indicates that many
connections exist among nodes in the network, while a low edge density
indicates that there are relatively few connections. In networks with
high edge density, information and resources are more likely to flow
freely among nodes, On the other hand, networks with low edge density
may be more fragmented or concentrated.
# Network/Class-level Network Measures====
#Density
cat("The density of trust graph is ", edge_density(trust_graph, loops = FALSE), "\n")## The density of trust graph is 0.1903846cat("The density of commnuication graph is ",edge_density(comm_graph_undirected, loops = FALSE), "\n")## The density of commnuication graph is 0.442674## The density of advice graph is 0.1567766Diameter refers to the maximum shortest path length
between any two nodes in the network. It is a measure of the longest
distance between any two nodes in the network.
## The diameter of trust graph is 10## The diameter of commnuication graph is 3## The diameter of advice graph is 5Average path length is calculated as the average of all
shortest path lengths between any two nodes in the network. Both
diameter and average path length provides
information on the overall efficiency and connectivity of the network.A
small average path length indicates that nodes in the network are
closely connected and can easily communicate and share information with
one another.
#APL Average Path Length
cat("The Average Path Length of trust graph is ", mean_distance(trust_graph, directed = TRUE, unconnected = TRUE), "\n")## The Average Path Length of trust graph is 4.072267cat("The Average Path Length of commnuication graph is ",mean_distance(comm_graph_undirected, directed = FALSE, unconnected = TRUE), "\n")## The Average Path Length of commnuication graph is 1.795421cat("The Average Path Length of advice graph is ",mean_distance(advice_graph, directed = TRUE, unconnected = TRUE), "\n")## The Average Path Length of advice graph is 2.077016Degree centrality measures the number of ties an node
has in a UNDIRECTED network . In-degree centrality measures
the number of incoming ties an node has in a DIRECTED
network.Out-degree centrality measures the number of
outgoing ties an individual has in a DIRECTED network.
[1] "Trust Graph Indegree Centrality Distribution" Min. 1st Qu. Median Mean 3rd Qu. Max.
0.009615 0.144231 0.173077 0.188370 0.240385 0.413461 [1] "Trust Graph Outdegree Centrality Distribution" Min. 1st Qu. Median Mean 3rd Qu. Max.
0.00000 0.04808 0.11538 0.18837 0.19231 1.00000 [1] "Advice Graph Indegree Centrality Distribution" Min. 1st Qu. Median Mean 3rd Qu. Max.
0.009615 0.115385 0.144231 0.155861 0.192308 0.548077 [1] "Advice Graph Outdegree Centrality Distribution" Min. 1st Qu. Median Mean 3rd Qu. Max.
0.00000 0.04808 0.07692 0.15586 0.17308 1.00000 [1] "Communication Graph Degree Centrality Distribution" Min. 1st Qu. Median Mean 3rd Qu. Max.
0.01923 0.33654 0.43269 0.44267 0.54808 0.86538 Betweenness centrality measures the extent to which an
individual lies on the shortest path between other pairs of individuals
in the network. Individuals with high betweenness centrality are more
likely to have access to diverse sources of information. Individuals
with low betweenness centrality are less central to the flow of
information and may be more isolated.
[1] "Trust Graph Betweenness Centrality Distribution" Min. 1st Qu. Median Mean 3rd Qu. Max.
0.0000000 0.0005134 0.0039476 0.0106551 0.0142215 0.0898118 [1] "Advice Graph Betweenness Centrality Distribution" Min. 1st Qu. Median Mean 3rd Qu. Max.
0.000000 0.001070 0.002979 0.009462 0.009678 0.115521 [1] "Communication Graph Betweenness Centrality Distribution" Min. 1st Qu. Median Mean 3rd Qu. Max.
0.000000 0.001164 0.003351 0.007312 0.008413 0.059016 Eigenvector centrality measures the extent to which an
individual is connected to other well-connected individuals in the
network. Individuals with high eigenvector centrality are well-connected
to other well-connected individuals in the network, and thus are more
likely to have influence over others in the network (i.e., greater power
and/or status).
[1] "Trust Graph Eigenvector Centrality Distribution" Min. 1st Qu. Median Mean 3rd Qu. Max.
0.01357 0.31493 0.43008 0.44923 0.57823 1.00000 [1] "Advice Graph Eigenvector Centrality Distribution" Min. 1st Qu. Median Mean 3rd Qu. Max.
0.01591 0.20917 0.29097 0.31562 0.39935 1.00000 [1] "Communication Graph Eigenvector Centrality Distribution" Min. 1st Qu. Median Mean 3rd Qu. Max.
0.01454 0.42456 0.54161 0.54445 0.67719 1.00000 Closeness centrality measures the extent to which an
individual is close to other individuals in the network, in terms of the
shortest path length.Individuals with high closeness centrality can more
easily access information and resources from others in the network.
[1] "Trust Graph Closeness Centrality Distribution" Min. 1st Qu. Median Mean 3rd Qu. Max.
0.5049 0.5591 0.5876 0.6158 0.6154 1.0000 [1] "Advice Graph Closeness Centrality Distribution" Min. 1st Qu. Median Mean 3rd Qu. Max.
0.5123 0.5417 0.5591 0.5831 0.5876 1.0000 [1] "Communication Graph Closeness Centrality Distribution" Min. 1st Qu. Median Mean 3rd Qu. Max.
0.4094 0.6012 0.6341 0.6473 0.6842 0.8814 #This function makes a data frame of individual statistics/network measures
graph_ind_stats<- function (class_network) {
#SNA_ids<-V(class_network)
bet<-betweenness(class_network, v = V(class_network), directed = TRUE, weights = NULL, normalized = T)
clo<-centr_clo(class_network, mode = c("total"), normalized = TRUE)$res
eig<-centr_eigen(class_network, directed = TRUE, scale = TRUE, normalized = TRUE)$vector
if (is_directed(class_network)){
indegree<-degree(class_network, v = V(class_network), mode = "in", loops = F, normalized = T)
outdegree<-degree(class_network, v = V(class_network), mode = "out", loops = F, normalized = T)
results<-as.data.frame(cbind(indegree,outdegree, bet,clo,eig))
names(results)<-c("indegree","outdegree", "betweenness","closeness","eigenvector")
results <- rownames_to_column(results, var = "SNA_ids")
}else {
degree<-degree(class_network, v = V(class_network), loops = F, normalized = T)
results<-as.data.frame(cbind(degree, bet,clo,eig))
names(results)<-c("degree", "betweenness","closeness","eigenvector")
results <- rownames_to_column(results, var = "SNA_ids")
}
return(results)
}
get_net_stats<- function (y, your_id){
x<-y[,-1]
class_stats<-sapply(x, function(x) c( "Stand dev" = round(sd(x),2),
"Mean"= round(mean(x,na.rm=TRUE),2),
"n" = length(x),
"Median" = round(median(x),2),
"Minimum" = round(min(x),2),
"Maximun" = round(max(x),2),
"Upper Quantile" = round(quantile(x,.75),2),
"LowerQuartile" = round(quantile(x,.25),2)
)
)
# print("******Class Statistics******")
print(class_stats)
# print("******YOUR Statistics******")
y[match(your_id, y$SNA_id),]
}
#Run function to get the statistics
advice_stats<-graph_ind_stats(advice_graph)
trust_stats<-graph_ind_stats(trust_graph)
comm_stats<-graph_ind_stats(comm_graph_undirected)In the tables below you may filter by your SNA_ID to find your corresponding values.
Where are you in the class advice network? Do you have a large or
small size of node? Do you know your centrality score? (Hint: by
selecting your node id from the drop down box and click on your own
node)
NOTE: You can resize the graphs and relocate individual
nodes.
# add node network attributes from network graph stats data from generated above
V(advice_graph)$betweenness <- advice_stats$betweenness
V(advice_graph)$indegree <- advice_stats$indegree
V(advice_graph)$outdegree <- advice_stats$outdegree
V(advice_graph)$eigenvector <- advice_stats$eigenvector
V(advice_graph)$closeness <- advice_stats$closeness
V(advice_graph)$value <- advice_stats$between
advice_graph<-set_graph_attr(advice_graph, "layout", layout_with_fr)
data <- toVisNetworkData(advice_graph)
node_df <- as.data.frame(data$nodes)
node_df <- node_df %>%
mutate(id = as.numeric(id)) %>%
arrange(id)
node_df$title = paste0("node id:",node_df$id,"</b><br>betweenness_centrality:", node_df$betweenness, "</b><br>eigenvector_centrality:",node_df$eigenvector,"</b><br>indegree_centrality:", node_df$indegree, "</b><br>outdegree_centrality:", node_df$outdegree, "</b><br>closeness_centrality:", node_df$closeness)
vn = visNetwork(node_df, edges = data$edges,height = "1500px", width = "150%") %>%
visConfigure(enabled = FALSE) %>%
visPhysics(enabled = FALSE, stabilization = FALSE) %>%
visIgraphLayout(layout = "layout.fruchterman.reingold") %>%
visLayout(randomSeed = 123)%>%
visOptions(
highlightNearest = list(enabled = TRUE, degree = 2, hover = TRUE),
nodesIdSelection = list(enabled = TRUE,
style = 'width: 200px; height: 26px;background: #f8f8f8;
color: darkblue;
border:none;
outline:none;'),
)
vn = visNodes(vn, id = data$nodes$id,
borderWidthSelected = 15,
color = list(highlight ="red"))
vn <- visEdges(vn, id = data$edges$id,
color = 'pink',
arrows = 'from')
vn# add node network attributes from network graph stats data fram generated above
V(trust_graph)$betweenness <- trust_stats$betweenness
V(trust_graph)$indegree <- trust_stats$indegree
V(trust_graph)$outdegree <- trust_stats$outdegree
V(trust_graph)$eigenvector <- trust_stats$eigenvector
V(trust_graph)$closeness <- trust_stats$closeness
V(trust_graph)$value <- trust_stats$betweenness
trust_graph<-set_graph_attr(trust_graph, "layout", layout_with_fr)
data <- toVisNetworkData(trust_graph)
node_df <- as.data.frame(data$nodes)
node_df$title = paste0("node id:",node_df$id,"</b><br>betweenness_centrality:", node_df$betweenness, "</b><br>eigenvector_centrality:",node_df$eigenvector,"</b><br>indegree_centrality:", node_df$indegree, "</b><br>outdegree_centrality:", node_df$outdegree, "</b><br>closeness_centrality:", node_df$closeness)
vn = visNetwork(node_df, edges = data$edges,height = "1500px", width = "200%") %>%
visConfigure(enabled = FALSE) %>%
visPhysics(enabled = FALSE, stabilization = FALSE) %>%
visIgraphLayout(layout = "layout.fruchterman.reingold") %>%
visLayout(randomSeed = 100) %>%
visOptions(highlightNearest =list(enabled = TRUE, hover = TRUE,degree = 3),
nodesIdSelection = list(enabled = TRUE,
style = 'width: 200px; height: 26px;
background: #f8f8f8;
color: darkblue;
border:none;
outline:none;'))
vn <- visNodes(vn, id = data$nodes$id,
borderWidthSelected = 15,
color = list(highlight ="red"))
vn <- visEdges(vn, id = data$edges$id,
color = 'pink',
arrows = 'from')
vn# add node network attributes from network graph stats data fram generated above
V(comm_graph_undirected)$betweenness <- comm_stats2$betweenness
V(comm_graph_undirected)$degree <- comm_stats2$degree
V(comm_graph_undirected)$eigenvector <- comm_stats2$eigenvector
V(comm_graph_undirected)$closeness <- comm_stats2$closeness
V(comm_graph_undirected)$value <- comm_stats2$betweenness
comm_graph_undirected<-set_graph_attr(comm_graph_undirected, "layout", layout_with_fr)
data <- toVisNetworkData(comm_graph_undirected)
node_df <- as.data.frame(data$nodes)
node_df$title = paste0("node id:",node_df$id,"</b><br>betweenness_centrality:", node_df$betweenness, "</b><br>eigenvector_centrality:",node_df$eigenvector,"</b><br>degree_centrality:",node_df$degree, "</b><br>closeness_centrality:", node_df$closeness)
vn = visNetwork(node_df, edges = data$edges,height = "1500px", width = "200%") %>%
visConfigure(enabled = FALSE) %>%
visPhysics(enabled = FALSE, stabilization = FALSE) %>%
visIgraphLayout(layout = "layout.fruchterman.reingold") %>%
visLayout(randomSeed = 123) %>%
visOptions(highlightNearest =list(enabled = TRUE, hover = TRUE,degree = 3),
nodesIdSelection = list(enabled = TRUE,
style = 'width: 200px; height: 26px;
background: #f8f8f8;
color: darkblue;
border:none;
outline:none;'))
vn = visNodes(vn, id = data$nodes$id,
borderWidthSelected = 6,
color = list(highlight ="red"))
vn <- visEdges(vn, id = data$edges$id,
color = 'pink')
vn