Comprehensive spectral approach for community structure analysis on complex networks

TL;DR

This paper presents a spectral method for analyzing community structures in complex networks by decomposing the adjacency matrix into components that reveal community and gateway link information, enabling automatic and flexible community detection.

Contribution

It introduces a universal spectral approach that works across all network types, providing a new way to identify communities and their overlaps automatically.

Findings

Effective community detection across various network types

Ability to identify overlapping communities and key gateway links

Provides measures of node affinity and antagonism

Abstract

A simple but efficient spectral approach for analyzing the community structure of complex networks is introduced. It works the same way for all types of networks, by spectrally splitting the adjacency matrix into a "unipartite" and a "multipartite" component. These two matrices reveal the structure of the network from different perspectives and can be analyzed at different levels of detail. Their entries, or the entries of their lower-rank approximations, provide measures of the affinity or antagonism between the nodes that highlight the communities and the "gateway" links that connect them together. An algorithm is then proposed to achieve the automatic assignment of the nodes to communities based on the information provided by either matrix. This algorithm naturally generates overlapping communities but can also be tuned to eliminate the overlaps.