A Generative Model for Controllable Feature Heterophily in Graphs

Haoyu Wang; Renyuan Ma; Gonzalo Mateos; Luana Ruiz

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arXiv · 2509.23230

A Generative Model for Controllable Feature Heterophily in Graphs

Haoyu Wang·Renyuan Ma·Gonzalo Mateos·Luana Ruiz

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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. These results elucidate how the interplay between the graphon and the filter governs the limiting level of feature heterophily, providing a tunable mechanism for data modeling and generation. We validate the theory through experiments demonstrating precise control of homophily across graph families and spectral filters.

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BibTeX RIS

Haoyu Wang, Renyuan Ma, Gonzalo Mateos, Luana Ruiz. 2025-09-27. A Generative Model for Controllable Feature Heterophily in Graphs. https://arxiv.org/abs/2509.23230

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