Estimating the number of communities in weighted networks

TL;DR

This paper introduces a new spectral clustering method combining weighted modularity to accurately estimate the number of communities in weighted and signed networks, addressing a key challenge in community detection.

Contribution

It proposes a novel approach that estimates the number of communities in weighted networks, including signed and negative weights, under a degree-corrected, distribution-free model.

Findings

The method outperforms existing techniques in accuracy.

It effectively handles negative and signed edge weights.

Numerical and empirical results validate its superiority.

Abstract

Community detection in weighted networks has been a popular topic in recent years. However, while there exist several flexible methods for estimating communities in weighted networks, these methods usually assume that the number of communities is known. It is usually unclear how to determine the exact number of communities one should use. Here, to estimate the number of communities for weighted networks generated from arbitrary distribution under the degree-corrected distribution-free model, we propose one approach that combines weighted modularity with spectral clustering. This approach allows a weighted network to have negative edge weights and it also works for signed networks. We compare the proposed method to several existing methods and show that our method is more accurate for estimating the number of communities both numerically and empirically.