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$_{\mathrm{Dbw}}$, 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$_{\mathrm{Dbw}}$ 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.
