Understanding Geopolitical Alignments Through Covariate Augmented Spectral Clustering of Heterogeneous UNGA Voting Data

Abstract

Community detection is a fundamental problem in network analysis. While many existing methods focus on homogeneous networks, real world networks are often heterogeneous, involving multiple node types and interaction mechanisms. In addition, node specific covariates frequently provide valuable information about the underlying community structure. Existing methodologies typically account for either network heterogeneity or covariate information, but seldom both simultaneously. In this paper, we propose a covariate assisted spectral clustering framework for heterogeneous networks that jointly utilizes network connectivity in a heterogeneous setting and node level covariates. The proposed method extends covariate assisted spectral clustering to heterogeneous settings and operates directly on the heterogeneous network without relying on projection based simplifications. Under a heterogeneous node contextualized stochastic blockmodel, we establish theoretical guarantees for the proposed procedure, including concentration results, eigenspace perturbation bounds, and an explicit upper bound on the misclustering rate. Simulation studies demonstrate that incorporating covariate information substantially improves community recovery and consistently outperforms several benchmark methods. We further apply the proposed framework to United Nations General Assembly voting data, where it reveals meaningful geopolitical structures by combining voting interactions with auxiliary covariate information.