How Powerful are K-hop Message Passing Graph Neural Networks

TL;DR

This paper analyzes the expressive power of K-hop message passing in Graph Neural Networks, showing it surpasses 1-WL but is limited compared to 3-WL, and introduces KP-GNN to enhance this power.

Contribution

The paper provides a theoretical characterization of K-hop message passing's expressive power, differentiates kernels, and proposes KP-GNN to improve graph discrimination capabilities.

Findings

K-hop message passing is more powerful than 1-WL.

K-hop message passing cannot distinguish some regular graphs, bounded by 3-WL.

KP-GNN effectively distinguishes many graphs previously indistinguishable.

Abstract

The most popular design paradigm for Graph Neural Networks (GNNs) is 1-hop message passing -- aggregating information from 1-hop neighbors repeatedly. However, the expressive power of 1-hop message passing is bounded by the Weisfeiler-Lehman (1-WL) test. Recently, researchers extended 1-hop message passing to K-hop message passing by aggregating information from K-hop neighbors of nodes simultaneously. However, there is no work on analyzing the expressive power of K-hop message passing. In this work, we theoretically characterize the expressive power of K-hop message passing. Specifically, we first formally differentiate two different kernels of K-hop message passing which are often misused in previous works. We then characterize the expressive power of K-hop message passing by showing that it is more powerful than 1-WL and can distinguish almost all regular graphs. Despite the higher expressive power, we show that K-hop message passing still cannot distinguish some simple regular graphs and its expressive power is bounded by 3-WL. To further enhance its expressive power, we introduce a KP-GNN framework, which improves K-hop message passing by leveraging the peripheral subgraph information in each hop. We show that KP-GNN can distinguish many distance regular graphs which could not be distinguished by previous distance encoding or 3-WL methods. Experimental results verify the expressive power and effectiveness of KP-GNN. KP-GNN achieves competitive results across all benchmark datasets.