Uplifting the Expressive Power of Graph Neural Networks through Graph Partitioning

• URL: http://arxiv.org/abs/2312.08671v1
• Date: Thu, 14 Dec 2023 06:08:35 GMT
• Title: Uplifting the Expressive Power of Graph Neural Networks through Graph Partitioning
• Authors: Asela Hevapathige, Qing Wang
• Abstract summary: We study the expressive power of graph neural networks through the lens of graph partitioning. We introduce a novel GNN architecture, namely Graph Partitioning Neural Networks (GPNNs)
• Score: 3.236774847052122
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Graph Neural Networks (GNNs) have paved its way for being a cornerstone in graph related learning tasks. From a theoretical perspective, the expressive power of GNNs is primarily characterised according to their ability to distinguish non-isomorphic graphs. It is a well-known fact that most of the conventional GNNs are upper-bounded by Weisfeiler-Lehman graph isomorphism test (1-WL). In this work, we study the expressive power of graph neural networks through the lens of graph partitioning. This follows from our observation that permutation invariant graph partitioning enables a powerful way of exploring structural interactions among vertex sets and subgraphs, and can help uplifting the expressive power of GNNs efficiently. Based on this, we first establish a theoretical connection between graph partitioning and graph isomorphism. Then we introduce a novel GNN architecture, namely Graph Partitioning Neural Networks (GPNNs). We theoretically analyse how a graph partitioning scheme and different kinds of structural interactions relate to the k-WL hierarchy. Empirically, we demonstrate its superior performance over existing GNN models in a variety of graph benchmark tasks.

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