Local multiresolution order in community detection

TL;DR

This paper introduces a local multiresolution approach for community detection in complex networks, enabling identification of well-defined local communities even when global structure is vague, by using correlation-based measures.

Contribution

It extends multiresolution community detection to a local level, providing measures to identify optimal resolutions for individual communities.

Findings

Effective in detecting local communities in constructed and real networks.

Method is independent of specific community detection algorithms.

Provides quantitative measures for community resolution quality.

Abstract

Community detection algorithms attempt to find the best clusters of nodes in an arbitrary complex network. Multi-scale ("multiresolution") community detection extends the problem to identify the best network scale(s) for these clusters. The latter task is generally accomplished by analyzing community stability simultaneously for all clusters in the network. In the current work, we extend this general approach to define local multiresolution methods, which enable the extraction of well-defined local communities even if the global community structure is vaguely defined in an average sense. Toward this end, we propose measures analogous to variation of information and normalized mutual information that are used to quantitatively identify the best resolution(s) at the community level based on correlations between clusters in independently-solved systems. We demonstrate our method on two constructed networks as well as a real network and draw inferences about local community strength. Our approach is independent of the applied community detection algorithm save for the inherent requirement that the method be able to identify communities across different network scales, with appropriate changes to account for how different resolutions are evaluated or defined in a particular community detection method. It should, in principle, easily adapt to alternative community comparison measures.