When Does the Silhouette Score Work? A Comprehensive Study in Network Clustering

TL;DR

This study evaluates the effectiveness of the silhouette score in network community detection, revealing its strengths and limitations across different network types and conditions, and providing practical guidance for its application.

Contribution

The paper offers a comprehensive empirical analysis of the silhouette score's performance in network clustering, clarifying when it is most reliable and highlighting its limitations.

Findings

Accurately detects communities in well-separated, balanced clusters

Underestimates in imbalanced or weakly separated clusters

Overestimates in sparse networks

Abstract

Selecting the number of communities is a fundamental challenge in network clustering. The silhouette score offers an intuitive, model-free criterion that balances within-cluster cohesion and between-cluster separation. Albeit its widespread use in clustering analysis, its performance in network-based community detection remains insufficiently characterized. In this study, we comprehensively evaluate the performance of the silhouette score across unweighted, weighted, and fully connected networks, examining how network size, separation strength, and community size imbalance influence its performance. Simulation studies show that the silhouette score accurately identifies the true number of communities when clusters are well separated and balanced, but it tends to underestimate under strong imbalance or weak separation and to overestimate in sparse networks. Extending the evaluation to a real airline reachability network, we demonstrate that the silhouette-based clustering can recover geographically interpretable and market-oriented clusters. These findings provide empirical guidance for applying the silhouette score in network clustering and clarify the conditions under which its use is most reliable.