Total communicability as a centrality measure

TL;DR

This paper introduces total communicability as a rapid and natural node centrality measure based on the exponential of the adjacency matrix, and compares it with existing measures through extensive numerical studies.

Contribution

It proposes total communicability as a new centrality measure and demonstrates its computational efficiency and effectiveness compared to subgraph and Katz centralities.

Findings

Total communicability can be computed rapidly even for large networks.

It provides a natural ranking of nodes based on their communicability.

Numerical studies show its effectiveness on synthetic and real-world networks.

Abstract

We examine a node centrality measure based on the notion of total communicability, defined in terms of the row sums of the exponential of the adjacency matrix of the network. We argue that this is a natural metric for ranking nodes in a network, and we point out that it can be computed very rapidly even in the case of large networks. Furthermore, we propose the total sum of node communicabilities as a useful measure of network connectivity. Extensive numerical studies are conducted in order to compare this centrality measure with the closely related ones of subgraph centrality [E. Estrada and J. A. Rodriguez-Velazquez, Phys. Rev. E, 71 (2005), 056103] and Katz centrality [L. Katz, Psychometrica, 18 (1953), pp. 39-43]. Both synthetic and real-world networks are used in the computations.