Archetypal Graph Generative Models: Explainable and Identifiable Communities via Anchor-Dominant Convex Hulls

TL;DR

GraphHull is an explainable graph generative model that uses convex hulls to identify and interpret community structures at multiple scales, improving interpretability and performance in network analysis tasks.

Contribution

The paper introduces GraphHull, a novel multi-level convex hull-based model that provides explainable community detection and link prediction in graphs, with scalable inference.

Findings

Successfully recovers multi-level community structures

Achieves competitive or superior link prediction performance

Provides natural interpretability of community roles

Abstract

Representation learning has been essential for graph machine learning tasks such as link prediction, community detection, and network visualization. Despite recent advances in achieving high performance on these downstream tasks, little progress has been made toward self-explainable models. Understanding the patterns behind predictions is equally important, motivating recent interest in explainable machine learning. In this paper, we present GraphHull, an explainable generative model that represents networks using two levels of convex hulls. At the global level, the vertices of a convex hull are treated as archetypes, each corresponding to a pure community in the network. At the local level, each community is refined by a prototypical hull whose vertices act as representative profiles, capturing community-specific variation. This two-level construction yields clear multi-scale explanations: a node's position relative to global archetypes and its local prototypes directly accounts for its edges. The geometry is well-behaved by design, while local hulls are kept disjoint by construction. To further encourage diversity and stability, we place principled priors, including determinantal point processes, and fit the model under MAP estimation with scalable subsampling. Experiments on real networks demonstrate the ability of GraphHull to recover multi-level community structure and to achieve competitive or superior performance in link prediction and community detection, while naturally providing interpretable predictions.