Communicability Graph and Community Structures in Complex Networks

TL;DR

This paper introduces a novel community detection method based on the communicability graph, extending the concept to weighted interactions and overlapping communities, demonstrated on the USA airport network.

Contribution

It proposes a new community detection algorithm using communicability graphs, incorporating interaction strength and overlapping community management.

Findings

Successfully identified distinct airport communities in the USA network.

Outperformed traditional algorithms in detecting meaningful community structures.

Extended communicability to weighted interactions using inverse temperature.

Abstract

We use the concept of the network communicability (Phys. Rev. E 77 (2008) 036111) to define communities in a complex network. The communities are defined as the cliques of a communicability graph, which has the same set of nodes as the complex network and links determined by the communicability function. Then, the problem of finding the network communities is transformed to an all-clique problem of the communicability graph. We discuss the efficiency of this algorithm of community detection. In addition, we extend here the concept of the communicability to account for the strength of the interactions between the nodes by using the concept of inverse temperature of the network. Finally, we develop an algorithm to manage the different degrees of overlapping between the communities in a complex network. We then analyze the USA airport network, for which we successfully detect two big communities of the eastern airports and of the western/central airports as well as two bridging central communities. In striking contrast, a well-known algorithm groups all but two of the continental airports into one community.