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.

翻译：图神经网络（GNNs）已成为图相关学习任务的基石。从理论角度而言，GNNs的表达能力主要根据其区分非同构图的能力来刻画。众所周知，大多数传统GNNs的表达能力上限受限于Weisfeiler-Lehman图同构测试（1-WL）。本文通过图划分的视角研究图神经网络的表达能力，这一研究思路源于我们的观察：置换不变的图划分为探索顶点集与子图间的结构交互提供了有效途径，并能够高效提升GNNs的表达能力。基于此，我们首先建立了图划分与图同构之间的理论联系，随后提出了一种新型GNN架构——图划分神经网络（GPNNs）。我们从理论上分析了图划分方案及不同结构交互类型与k-WL层级结构的关系，并通过实验证明该模型在多种图基准任务中相较于现有GNN模型具有更优性能。