Defining Least Community as a Homogeneous Group in Complex Networks

TL;DR

This paper proposes a novel community detection method based on homogeneity and heterogeneity, utilizing head/tail breaks and edge betweenness, revealing power-law distributions of community sizes in complex networks.

Contribution

It introduces the concept of least community as a homogeneous group and develops a new detection algorithm leveraging heavy-tailed distributions and head/tail breaks.

Findings

Communities follow power-law size distributions.

More small communities than large ones are identified.

The method reveals fundamental scaling properties in networks.

Abstract

This paper introduces a new concept of least community that is as homogeneous as a random graph, and develops a new community detection algorithm from the perspective of homogeneity or heterogeneity. Based on this concept, we adopt head/tail breaks - a newly developed classification scheme for data with a heavy-tailed distribution - and rely on edge betweenness given its heavy-tailed distribution to iteratively partition a network into many heterogeneous and homogeneous communities. Surprisingly, the derived communities for any self-organized and/or self-evolved large networks demonstrate very striking power laws, implying that there are far more small communities than large ones. This notion of far more small things than large ones constitutes a new fundamental way of thinking for community detection. Keywords: head/tail breaks, ht-index, scaling, k-means, natural breaks, and classification