A Generative Model for Controllable Feature Heterophily in Graphs

ABSTRACT We introduce a principled generative framework for graph signals that enables explicit control of feature heterophily, a key property underlying the effectiveness of graph learning methods. Our model combines a Lipschitz graphon-based random graph generator with Gaussian node features filtered through a smooth spectral function of the rescaled Laplacian. We establish new theoretical guarantees: (i) a concentration result for the empirical heterophily score; and (ii) almost-sure convergence of the feature heterophily measure to a deterministic functional of the graphon degree profile, based on a graphon-limit law for polynomial averages of Laplacian eigenvalues. Index T erms-- graph generative models, homophily, graphons 1. INTRODUCTION The success of many graph information processing problems, including node-level tasks in graph machine learning [1, 2] and network topology inference [3-5], hinges on the alignment between graph topology and node features, often summarized by the notion of homophily or heterophily. We develop a generative framework for graphs and node features (i.e., graph signals) that allows explicit control of feature het-erophily in the range from homophily to heterophily.