19.1

19.1 (p. 476). Describing a network. Consider an undirected network for individuals A, B, C, D, and E. - A is connected to B and C. - B is connected to A and C. - C is connected to A, B, and D. - D is connected to C, and E. - E is connected to D.

Produce a network graph for this network.

library(igraph)


Attaching package: ‘igraph’

The following objects are masked from ‘package:stats’:

    decompose, spectrum

The following object is masked from ‘package:base’:

    union

edges <- rbind(
  c("A", "B"), c("A", "C"),
  c("B", "A"), c("B", "C"),
  c("C", "A"), c("C", "B"), c("C", "D"), 
  c("D", "C"), c("D", "E"),
  c("E", "D")
)
graph <- graph.edgelist(edges, directed = FALSE)
plot(graph, vertex.size = 1, vertex.label.dist = 0.5)

B. What node(s) would need to be removed from the graph for the remaining nodes to consititue a clique?

Answer: nodes D and E should be removed.

# "A clique is a network in which each node is directly connected by an edge to every other node" (c) textbook 19.4 page 462.
clique <- delete_vertices(graph, c("D", "E"))
plot(clique, vertex.size = 1, vertex.label.dist = 0.5)

C. What is the degree for node A?

Answer: 4

(graph.degrees <- degree(graph))

A B C D E 
4 4 6 4 2

D. Which node(s) have the lowest degree?

Answer: Node E. It has degree of 2.

E. Tabulate the degree distribution for this network

graph.degree_distr <- degree_distribution(graph)
plot(seq(0, max(graph.degrees)), graph.degree_distr * 10, 
     xlab="degree vertices", ylab="frequency", 
     main="Degree distribution")

F. Is this network connected?

Answer: Yes, it is connected, since each node in the network has a path to another node.

G. Calculate betweenness centrality for nodes A and C.

Answer: A = 0; C = 4

( graph.betweenness <- betweenness(graph) )

A B C D E 
0 0 4 3 0

H. Calculate the density of the network.

Answer: 1

# desity for undirected graph:
e <- gsize(graph)
n <- length(V(graph))
( graph.density <- e/(n*(n-1)/2) )

[1] 1

# also can be found through:
#(graph.density <- edge_density(graph))

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