Multiresolution community detection for megascale networks by information-based replica correlations

TL;DR

This paper introduces a multiresolution community detection method using information-based replica correlations, capable of analyzing megascale networks with high accuracy and avoiding common resolution limits.

Contribution

The authors develop a Potts model-based multiresolution algorithm that quantifies hierarchical structures in large graphs using replica correlations and information measures.

Findings

Accurately detects multilevel community structures in graphs with over 40 million nodes.

Avoids the resolution limit affecting other models.

Scales super-linearly with network size, enabling analysis of very large systems.

Abstract

We use a Potts model community detection algorithm to accurately and quantitatively evaluate the hierarchical or multiresolution structure of a graph. Our multiresolution algorithm calculates correlations among multiple copies ("replicas") of the same graph over a range of resolutions. Significant multiresolution structures are identified by strongly correlated replicas. The average normalized mutual information, the variation of information, and other measures in principle give a quantitative estimate of the "best" resolutions and indicate the relative strength of the structures in the graph. Because the method is based on information comparisons, it can in principle be used with any community detection model that can examine multiple resolutions. Our approach may be extended to other optimization problems. As a local measure, our Potts model avoids the "resolution limit" that affects other popular models. With this model, our community detection algorithm has an accuracy that ranks among the best of currently available methods. Using it, we can examine graphs over 40 million nodes and more than one billion edges. We further report that the multiresolution variant of our algorithm can solve systems of at least 200000 nodes and 10 million edges on a single processor with exceptionally high accuracy. For typical cases, we find a super-linear scaling, O(L^{1.3}) for community detection and O(L^{1.3} log N) for the multiresolution algorithm where L is the number of edges and N is the number of nodes in the system.