Communicability in complex networks

TL;DR

This paper introduces a new measure of network communicability that accounts for non-shortest paths, revealing structural and dynamic properties of complex networks, including community detection and classification into universality classes.

Contribution

It proposes a broad generalization of communicability in networks, enabling analysis of non-shortest paths, community detection, and classification of networks based on structure-dynamic correlations.

Findings

Most real-world networks show high communicability among highly connected nodes.

Some networks exhibit disassortative communicability with poor communication between popular nodes.

The new measure distinguishes finer network structures like communities.

Abstract

Many topological and dynamical properties of complex networks are defined by assuming that most of the transport on the network flows along the shortest paths. However, there are different scenarios in which non-shortest paths are used to reach the network destination. Thus the consideration of the shortest paths only does not account for the global communicability of a complex network. Here we propose a new measure of the communicability of a complex network, which is a broad generalization of the concept of the shortest path. According to the new measure, most of real-world networks display the largest communicability between the most connected (popular) nodes of the network (assortative communicability). There are also several networks with the disassortative communicability, where the most "popular" nodes communicate very poorly to each other. Using this information we classify a diverse set of real-world complex systems into a small number of universality classes based on their structure-dynamic correlation. In addition, the new communicability measure is able to distinguish finer structures of networks, such as communities into which a network is divided. A community is unambiguously defined here as a set of nodes displaying larger communicability among them than to the rest of nodes in the network.