Approximate Conditional Sampling for Pattern Detection in Weighted Networks

TL;DR

This paper introduces a null model and an MCMC sampling algorithm for assessing the significance of patterns in weighted networks, addressing a gap in existing unweighted graph models.

Contribution

It proposes a new null model fixing node strengths exactly and node degrees approximately, along with a novel MCMC method for sampling and significance testing.

Findings

Model compares favorably to alternatives in detecting subtle patterns

Algorithm effectively evaluates community structure significance

Empirical results demonstrate robustness of the approach

Abstract

Assessing the statistical significance of network patterns is crucial for understanding whether such patterns indicate the presence of interesting network phenomena, or whether they simply result from less interesting processes, such as nodal-heterogeneity. Typically, significance is computed with reference to a null model. While there has been extensive research into such null models for unweighted graphs, little has been done for the weighted case. This article suggests a null model for weighted graphs. The model fixes node strengths exactly, and approximately fixes node degrees. A novel MCMC algorithm is proposed for sampling the model, and its stochastic stability is considered. We show empirically that the model compares favorably to alternatives, particularly when network patterns are subtle. We show how the algorithm can be used to evaluate the statistical significance of community structure.