Significant Scales in Community Structure

TL;DR

This paper introduces a novel, efficient approach to identify significant community structures at various scales in complex networks, using a new measure of partition significance based on subgraph probabilities.

Contribution

The authors propose a new method for detecting significant community scales and a measure of significance that is applicable across different detection techniques.

Findings

The method successfully identifies meaningful community resolutions in benchmark networks.

Optimizing significance enhances community detection performance.

Application to European Parliament data reveals increased ideological division over time.

Abstract

Many complex networks show signs of modular structure, uncovered by community detection. Although many methods succeed in revealing various partitions, it remains difficult to detect at what scale some partition is significant. This problem shows foremost in multi-resolution methods. We here introduce an efficient method for scanning for resolutions in one such method. Additionally, we introduce the notion of "significance" of a partition, based on subgraph probabilities. Significance is independent of the exact method used, so could also be applied in other methods, and can be interpreted as the gain in encoding a graph by making use of a partition. Using significance, we can determine "good" resolution parameters, which we demonstrate on benchmark networks. Moreover, optimizing significance itself also shows excellent performance. We demonstrate our method on voting data from the European Parliament. Our analysis suggests the European Parliament has become increasingly ideologically divided and that nationality plays no role.