Empirical likelihood test for community structure in networks

TL;DR

This paper introduces two new statistical tests, the WST and EL tests, for detecting community structure in both weighted and unweighted networks, especially effective for small networks.

Contribution

The paper develops the first empirical likelihood test for community detection applicable to weighted and unweighted networks, improving performance on small networks.

Findings

EL test may outperform WST for small networks

Both tests outperform existing methods on small networks

Applicable to weighted and unweighted networks

Abstract

Network data, characterized by interconnected nodes and edges, is pervasive in various domains and has gained significant popularity in recent years. In network data analysis, testing the presence of community structure in a network is one of the important research tasks. Existing tests are mainly developed for unweighted networks. In this paper, we study the problem of testing the existence of community structure in general (either weighted or unweighted) networks. We propose two new tests: the Weighted Signed-Triangle (WST) test and the empirical likelihood (EL) test. Both tests can be applied to weighted or unweighted networks and outperform existing tests for small networks. The EL test may outperform the WST test for small networks.