Significance-based community detection in weighted networks

TL;DR

This paper introduces a new null model for weighted networks, the continuous configuration model, and develops a community detection algorithm called CCME that incorporates hypothesis testing, demonstrating competitive performance on simulations and real-world networks.

Contribution

The paper presents the continuous configuration model as a null for weighted networks and integrates it into a community detection algorithm with proven theoretical properties.

Findings

CCME performs well in detecting communities with overlapping structures.

The method is effective in networks with background nodes.

Theoretical guarantees include a central limit theorem and asymptotic consistency.

Abstract

Community detection is the process of grouping strongly connected nodes in a network. Many community detection methods for un-weighted networks have a theoretical basis in a null model. Communities discovered by these methods therefore have interpretations in terms of statistical signficance. In this paper, we introduce a null for weighted networks called the continuous configuration model. We use the model both as a tool for community detection and for simulating weighted networks with null nodes. First, we propose a community extraction algorithm for weighted networks which incorporates iterative hypothesis testing under the null. We prove a central limit theorem for edge-weight sums and asymptotic consistency of the algorithm under a weighted stochastic block model. We then incorporate the algorithm in a community detection method called CCME. To benchmark the method, we provide a simulation framework incorporating the null to plant "background" nodes in weighted networks with communities. We show that the empirical performance of CCME on these simulations is competitive with existing methods, particularly when overlapping communities and background nodes are present. To further validate the method, we present two real-world networks with potential background nodes and analyze them with CCME, yielding results that reveal macro-features of the corresponding systems.