A network community structure similarity index for weighted networks

Identification of communities in complex systems is an essential part of network analysis. Accordingly, measuring similarities between communities is a fundamental part of analysing community structure in different, yet related, networks. Commonly used methods for quantifying network community similarity fail to consider the effects of edge weights. Existing methods remain limited when the two networks being compared have different numbers of nodes. In this study, we address these issues by proposing a novel network community structure similarity index (NCSSI) based on the edit distance concept. NCSSI is proposed as a similarity index for comparing network communities. The NCSSI incorporates both community labels and edge weights. The NCSSI can also be employed to assess the similarity between two communities with varying numbers of nodes. We test the proposed method using simulated data and case-study analysis of New York Yellow Taxi flows and compare the results with that of other commonly used methods (i.e., mutual information and the Jaccard index). Our results highlight how NCSSI effectively captures the impact of both label and edge weight changes and their impacts on community structure, which are not captured in existing approaches. In conclusion, NCSSI offers a new approach that incorporates both label and weight variations for community similarity measurement in complex networks.