Statistical test for detecting community structure in real-valued edge-weighted graphs

TL;DR

This paper introduces a new statistical test for detecting community structures in real-valued edge-weighted graphs, leveraging the Wigner semicircular law to analyze eigenvalue distributions.

Contribution

It presents a novel method based on spectral properties and provides theoretical and empirical validation, outperforming existing techniques.

Findings

The method effectively detects community structures in synthetic data.

It outperforms state-of-the-art methods in real data experiments.

Theoretical foundation based on Wigner semicircular law supports its validity.

Abstract

We propose a novel method to test the existence of community structure of undirected real-valued edge-weighted graph. The method is based on Wigner semicircular law on the asymptotic behavior of the random distribution for eigenvalues of a real symmetric matrix. We provide a theoretical foundation for this method and report on its performance in synthetic and real data, suggesting that our method outperforms other state-of-the-art methods.