Centrality Measures in Network Analysis

Centrality measures are crucial in network analysis as they provide insights into the individual characteristics of nodes (vertices) within a network. In this exercise, we will explore three key centrality measures: degree, closeness, and betweenness. We will use the network package from the statnet suite to create and analyze a network.

Network Creation

First, let’s create a network. We will use an adjacency matrix to represent the connections between nodes. Each row and column represent a node, and a value of 1 indicates a connection between the corresponding nodes.

netmat <- rbind(c(0,1,1,0,0,0,0,0,0,0),
                c(1,0,1,0,0,0,0,0,0,0),
                c(1,1,0,1,1,0,1,0,0,0),
                c(0,0,1,0,1,0,0,0,0,0),
                c(0,0,1,1,0,1,0,0,0,0),
                c(0,0,0,0,1,0,1,0,0,0),
                c(0,0,1,0,0,1,0,1,0,0),
                c(0,0,0,0,0,0,1,0,1,1),
                c(0,0,0,0,0,0,0,1,0,0),
                c(0,0,0,0,0,0,0,1,0,0))

rownames(netmat) <- c("A","B","C","D","E","F","G","H","I","J")
colnames(netmat) <- c("A","B","C","D","E","F","G","H","I","J")
net <- network(netmat)

Degree Centrality

Degree centrality refers to the number of edges that are adjacent to a certain vertex. In other words, it measures the number of direct connections a node has.

degree(net, gmode="graph")

The output is as follows:

2 2 5 2 3 2 3 3 1 1

Closeness Centrality

Closeness centrality measures the average length of the shortest paths from a node to all other nodes in the network. It indicates how close a node is to all other nodes in the network.

closeness(net, gmode = "graph")

The output is shown below:

0.4090909 0.4090909 0.6000000 0.4285714 0.4500000 0.4500000 0.6000000 0.4736842 0.3333333 0.3333333

Betweenness Centrality

Betweenness centrality quantifies the number of times a node acts as a bridge along the shortest path between two other nodes. It measures the influence of a node over the flow of information in the network.

betweenness(net, gmode="graph")

0.0  0.0 20.0  0.0  2.5  2.0 19.5 15.0  0.0  0.0