Ego-GNNs: Exploiting Ego Structures in Graph Neural Networks

TL;DR

Ego-GNNs enhance traditional GNNs by incorporating local ego graph structures, enabling recognition of complex subgraphs like triangles and improving node classification performance on synthetic and real datasets.

Contribution

This paper introduces Ego-GNNs, a novel method that augments message-passing with ego graph information, surpassing the limitations of standard GNNs in recognizing substructures.

Findings

Ego-GNNs can recognize triangles in graphs, unlike traditional GNNs.

Experimental results show improved node classification accuracy.

Ego-GNNs are more powerful in capturing local graph structures.

Abstract

Graph neural networks (GNNs) have achieved remarkable success as a framework for deep learning on graph-structured data. However, GNNs are fundamentally limited by their tree-structured inductive bias: the WL-subtree kernel formulation bounds the representational capacity of GNNs, and polynomial-time GNNs are provably incapable of recognizing triangles in a graph. In this work, we propose to augment the GNN message-passing operations with information defined on ego graphs (i.e., the induced subgraph surrounding each node). We term these approaches Ego-GNNs and show that Ego-GNNs are provably more powerful than standard message-passing GNNs. In particular, we show that Ego-GNNs are capable of recognizing closed triangles, which is essential given the prominence of transitivity in real-world graphs. We also motivate our approach from the perspective of graph signal processing as a form of multiplex graph convolution. Experimental results on node classification using synthetic and real data highlight the achievable performance gains using this approach.