Cluster Validity across Attribute and Network Spaces: Empirical Benchmarks for Attributed Networks Clustering

Abstract We empirically study internal cluster validity indices for attributed networks by evaluating feature- and network-space criteria under controlled generators that decouple attributes from topology while sharing cluster cardinalities. Using unified notation, Gaussian blobs for features, and a stochastic block model for graphs, we assess Silhouette Width (SW), Calinski–Harabasz (CH), Davies–Bouldin (DBI), $${{S}_{{{\text{Dbw}}}}}$$ , Average Isolability (AVI), Average Unifiability (AVU), and ANUI on both ground-truth and random partitions. SW is stable and saturates once enough features are present; CH grows strongly with sample size (suggesting reporting CH/N); DBI and $${{S}_{{{\text{Dbw}}}}}$$ separate ground truth from random partitions but have K -dependent random baselines, motivating baseline normalization. In network space, AVI increases with assortativity and decreases roughly as 1/ K , AVU drops with K toward a floor, and ANUI follows these trends; all indices approach random baselines as overlap/mixing increases, while confidence intervals narrow with more samples or informative features. We provide an empirical benchmark, simple scaling heuristics, and practical guidance for applying CVIs in attributed networks.