Beyond 1-WL with Local Ego-Network Encodings

Nurudin Alvarez-Gonzalez, Andreas Kaltenbrunner, Vicenç Gómez

Keywords: GNNs, message passing, weisfeiler-lehman, ego-networks, expressivity

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.

Type Of Submission: Extended abstract (max 4 main pages).

Type Of Submission: Extended abstract.

Software: https://github.com/nur-ag/IGEL

Community Implementations: [ 2 code implementations](https://www.catalyzex.com/paper/arxiv:2211.14906/code)