Scaling Higher-Order Graph Learning with Maximal Clique Complexes

Antoine Vialle, Aref Einizade, Fragkiskos D. Malliaros, Jhony H. Giraldo

Keywords: Graph Neural Networks, Topological Neural Networks, Random walks on cliques, Scalability, Cellular Neural Networks

Abstract:

Graph neural networks (GNNs) are widely used for learning on graphs but are fundamentally limited to modeling pairwise relationships.
Topological models based on simplicial or cell complexes can capture higher-order structure and match or surpass the expressive power of the Weisfeiler–Leman (WL) test, but they are difficult to scale because they require constructing higher-order complexes.
In this paper, we ask how to retain the expressivity of cellular Weisfeiler networks (CWNs) while improving their scalability, and how to exploit cliques efficiently on large graphs. First, we introduce simplified and factored cellular Weisfeiler–Leman (sCWL and fCWL) tests, and show that they are as expressive as the original CWL test, while achieving better scalability properties. We then define the maximal clique complex, a cell complex whose higher-order cells are the maximal cliques of the graph, and apply the corresponding simplified and factored CWNs (sCWN and fCWN) on this structure, achieving improved time and memory complexity. To avoid explicit enumeration of all maximal cliques, we propose CliqueWalk, a biased random walk that samples (maximal) cliques and scales quasi-linearly with the number of nodes.
Combining maximal clique complexes with CliqueWalk yields scalable clique-based architectures that preserve CWL-level expressivity.
Experiments on node and graph classification benchmarks, including large-scale datasets, show that our models are competitive with or better than GNN and higher-order baselines, while substantially reducing computational and memory costs.

Primary Area: learning on graphs and other geometries & topologies

Submission Number: 16681