Covariate Connectivity Combined Clustering for Weighted Networks

TL;DR

The paper introduces C4, an adaptive spectral clustering method that effectively combines network connectivity and node attributes for community detection in weighted networks, improving accuracy and scalability.

Contribution

It proposes a novel covariate connectivity combined clustering algorithm that adaptively integrates node covariates with network structure without requiring prior knowledge of the number of communities.

Findings

C4 outperforms existing methods in accuracy and robustness in simulations.

The method effectively estimates the number of communities using an eigengap heuristic.

Application to real-world networks demonstrates scalability and practical utility.

Abstract

Community detection is a central task in network analysis, with applications in social, biological, and technological systems. Traditional algorithms rely primarily on network topology, which can fail when community signals are partly encoded in node-specific attributes. Existing covariate-assisted methods often assume the number of clusters is known, involve computationally intensive inference, or are not designed for weighted networks. We propose $\text{C}^4$: Covariate Connectivity Combined Clustering, an adaptive spectral clustering algorithm that integrates network connectivity and node-level covariates into a unified similarity representation. $\text{C}^4$ balances the two sources of information through a data-driven tuning parameter, estimates the number of communities via an eigengap heuristic, and avoids reliance on costly sampling-based procedures. Simulation studies show that $\text{C}^4$ achieves higher accuracy and robustness than competing approaches across diverse scenarios. Application to an airport reachability network demonstrates the method's scalability, interpretability, and practical utility for real-world weighted networks.