Community detection based on significance optimization in complex networks

TL;DR

This paper investigates the significance measure for community detection in complex networks, analyzing its behavior, critical points, and phase transitions, and demonstrates that significance optimization offers higher resolution but risks over-splitting communities.

Contribution

It provides a detailed theoretical analysis of the significance measure, including formulas for critical points and phase diagrams, and validates findings with experiments using Louvain algorithm.

Findings

Critical number of communities increases with link density differences.

Significance optimization offers higher resolution than many methods.

It can lead to excessive community splitting.

Abstract

Community structure is an important structural property that extensively exists in various complex networks. In the past decade, much attention has been paid to the design of community-detection methods, but analyzing the behaviors of the methods is also of interest in the theoretical research and real applications. Here, we focus on an important measure for community structure, significance [Sci. Rep. 3 (2013) 2930]. Specifically, we study the effect of various network parameters on this measure in detail, analyze the critical behaviors of it in partition transition, and analytically give the formula of the critical points and the phase diagrams. The results shows that the critical number of communities in partition transition increases dramatically with the difference between inter- and intra-community link densities, and thus significance optimization displays higher resolution in community detection than many other methods, but it is also easily to lead to the excessive splitting of communities. By Louvain algorithm for significance optimization, we confirmed the theoretical results on artificial and real-world networks, and give a series of comparisons with some classical methods.