Analysis of Complex Networks

4.3 Spectral Measures of Node Centrality

A local characterization of networks is made numerically by using one of several measures known as “centrality” [14]. One of the most used centrality measures is the “degree centrality” (DC) [15], which can be interpreted as a measure of immediate influence, as opposed to long-term effect, in a network [14]. Several other centrality measures have been introduced and studied for real-world networks, in particular for social networks. They account for the different node characteristics that permit them to be ranked in order of importance in the network. Betweenness centrality (BC) measures the number of times that a shortest path between nodes i and j travels through anode k whose centrality is being measured. The farness of a vertex is the sum of the lengths of the geodesics to every other vertex. The inverse of farness is closeness centrality (CC).

The first spectral measure of centrality was introduced by Bonacich in 1987 as the eigenvector centrality (EC) [16]. This centrality measure is not restricted to shortest paths [16]; it is defined as the principal or dominant eigenvector of the adjacency matrix A representing the connected subgraph or component of a network. It simulates a mechanism in which each node affects all of its neighbors simultaneously [17]. EC is better interpreted as a sort of extended-degree centrality that is proportional to the sum of the centralities of the node neighbors. Consequently, a node has a high value of ...