Beyond 1-WL with Local Ego-Network Encodings

TL;DR

This paper introduces IGEL, a novel encoding method based on ego-networks that enhances graph neural networks' ability to distinguish complex graph structures beyond the traditional 1-WL test, improving performance across multiple architectures.

Contribution

The paper presents IGEL, a new preprocessing technique that encodes ego-networks to significantly increase GNNs' expressivity beyond 1-WL, with formal analysis and empirical validation.

Findings

IGEL matches state-of-the-art isomorphism detection performance.

IGEL improves accuracy across seven GNN architectures.

The method extends GNN expressivity beyond 1-WL limitations.

Abstract

Identifying similar network structures is key to capture graph isomorphisms and learn representations that exploit structural information encoded in graph data. This work shows that ego-networks can produce a structural encoding scheme for arbitrary graphs with greater expressivity than the Weisfeiler-Lehman (1-WL) test. We introduce IGEL, a preprocessing step to produce features that augment node representations by encoding ego-networks into sparse vectors that enrich Message Passing (MP) Graph Neural Networks (GNNs) beyond 1-WL expressivity. We describe formally the relation between IGEL and 1-WL, and characterize its expressive power and limitations. Experiments show that IGEL matches the empirical expressivity of state-of-the-art methods on isomorphism detection while improving performance on seven GNN architectures.