Constant Communities in Complex Networks

TL;DR

This paper introduces the concept of constant communities in complex networks, showing their invariance to vertex ordering and their potential to stabilize community detection results, with a case study on phoneme networks.

Contribution

It identifies and analyzes invariant groups of vertices, called constant communities, and demonstrates their utility in improving community detection stability.

Findings

Constant communities' percentage varies across applications.

Using constant communities reduces variability in detection results.

Constant communities form core functional units in phoneme networks.

Abstract

Identifying community structure is a fundamental problem in network analysis. Most community detection algorithms are based on optimizing a combinatorial parameter, for example modularity. This optimization is generally NP-hard, thus merely changing the vertex order can alter their assignments to the community. However, there has been very less study on how vertex ordering influences the results of the community detection algorithms. Here we identify and study the properties of invariant groups of vertices (constant communities) whose assignment to communities are, quite remarkably, not affected by vertex ordering. The percentage of constant communities can vary across different applications and based on empirical results we propose metrics to evaluate these communities. Using constant communities as a pre-processing step, one can significantly reduce the variation of the results. Finally, we present a case study on phoneme network and illustrate that constant communities, quite strikingly, form the core functional units of the larger communities.