Selecting representative community partitions under modularity degeneracy: the STAR method

TL;DR

The paper introduces the STAR method, a simple post-processing technique to select representative community partitions from degenerate modularity solutions, improving stability and interpretability across various network types.

Contribution

It proposes a model-agnostic, easy-to-implement approach for choosing representative partitions in modularity degeneracy, applicable to signed and unsigned networks without extra optimization.

Findings

The STAR method produces highly consistent community partitions.

It outperforms consensus clustering in simplicity and applicability.

Applicable to networks with positive and negative weights.

Abstract

Community detection based on modularity maximization is one of the most widely used approaches for uncovering mesoscale structures in complex networks. However, it is well known that the modularity function exhibits a highly degenerate optimization landscape: a large number of structurally distinct partitions attain close modularity values. This degeneracy raises issues of instability, reproducibility, and interpretability of the detected communities. We propose a simple and user-friendly post-processing method to address this problem by selecting a representative partition among the set of high-modularity solutions. The proposed approach is model-agnostic and can be applied a posteriori to the output of any modularity-based community detection algorithm. Rather than seeking the optimal partition in terms of modularity, our method aims to identify a solution that best represents the structural features shared across degenerate partitions. We compare our approach with consensus clustering methods, which pursue a similar objective, and show that the resulting partitions are highly consistent, while being obtained through a substantially simpler procedure that does not require additional optimization steps or external software packages. Moreover, unlike standard consensus clustering techniques, the proposed method can be applied to networks with both positive and negative edge weights, making it suitable for a wide range of applications involving signed networks and correlation-based systems, such as social, financial, and neuroscience networks. Overall, the method provides a practical and robust tool for handling degeneracy in modularity-based community detection, combining simplicity with broad applicability across different types of networks and real-world problems.