Week 4 Challenge Instructions

Centrality of a Network

Challenge Overview

Describe the many measures of centrality of at least one network of your choice.

Describe the Network Data

If you have not done it before, always start by evaluating the basic structure of the network (number of edges and vertices, dyad and triad census, etc.). Create a data frame nodes with the corresponding local attributes such as degree or local transitivity.

Centrality

Compute at least one measure of centrality for each node, adding them as attributes to nodes in the form of extra columns: eigencentrality, betweenness, closeness, etc. Compute the distribution of at least one of those measures. What do we learn from comparing these measures of centrality with an equivalent random network (i.e. with the same number of edges and vertices)?

Code

got_marriages <- read.csv("C:/Users/18639/Social_Networks_Spring_2023/posts/_data/got/got_marriages.csv")

Code

graph <- graph_from_edgelist(as.matrix(got_marriages[, c("From", "To")]))

Code

nodes <- data.frame("Name"=c(), "degree"=c(), "transitivity"=c(), 'centrality'=c())
families <- unique.data.frame(as.data.frame(got_marriages[, c("To")]))
centrality <- eigen_centrality(graph)$vector

# Iterate across family names computing degrees
for (name in families) {
  obs <- data.frame("Name"=name, "degree"=degree(graph, v = name, mode = "total"), "transitivity"=transitivity(graph, vids=name, type="local"), "centrality"=centrality[name])

  nodes <- rbind(nodes, obs)
}
nodes

                   Name degree transitivity  centrality
Stark             Stark     34    0.4166667 0.113194498
Martell         Martell     12    0.4000000 0.089478716
Essos             Essos     15    0.6000000 0.192767892
Reach             Reach     49    0.3636364 0.282784492
Septa             Septa      1          NaN 0.001889578
Dorne             Dorne      4    1.0000000 0.046014412
Targaryen     Targaryen     85    0.3636364 1.000000000
Lannister     Lannister     28    0.7000000 0.057273778
Vale               Vale     37    0.4666667 0.151988690
Riverlands   Riverlands     39    0.5714286 0.299362265
Crownlands   Crownlands     22    0.5714286 0.272772860
Westerlands Westerlands     31    0.6666667 0.089262517
Tyrell           Tyrell     12    1.0000000 0.055324132
North             North     46    0.1666667 0.126568322
Beyond Wall Beyond Wall      1          NaN 0.002672823
Frey               Frey     51    0.2888889 0.214820599
Tully             Tully      5    0.5000000 0.018146747
Stormlands   Stormlands     11    0.7000000 0.099655003
Arryn             Arryn     10    0.6666667 0.079951432
Baratheon     Baratheon     17    0.4181818 0.089383036

Code

random_network <- sample_gnp(length(V(graph)), graph.density(graph))
plot(random_network)

Code

hist(nodes$centrality)

Code

hist(eigen_centrality(random_network)$vector)