Ego-based Entropy Measures for Structural Representations on Graphs

TL;DR

This paper introduces VNEstruct, a novel, efficient entropy-based method for generating structural graph representations that are robust and achieve state-of-the-art results in classification tasks without relying on traditional GNNs.

Contribution

VNEstruct provides a simple, low-complexity approach for structural node representation using neighborhood entropy measures, outperforming existing methods in robustness and accuracy.

Findings

VNEstruct is robust to graph perturbations.

Achieves state-of-the-art performance in graph classification.

Operates efficiently without high time and space complexity.

Abstract

Machine learning on graph-structured data has attracted high research interest due to the emergence of Graph Neural Networks (GNNs). Most of the proposed GNNs are based on the node homophily, i.e neighboring nodes share similar characteristics. However, in many complex networks, nodes that lie to distant parts of the graph share structurally equivalent characteristics and exhibit similar roles (e.g chemical properties of distant atoms in a molecule, type of social network users). A growing literature proposed representations that identify structurally equivalent nodes. However, most of the existing methods require high time and space complexity. In this paper, we propose VNEstruct, a simple approach, based on entropy measures of the neighborhood's topology, for generating low-dimensional structural representations, that is time-efficient and robust to graph perturbations. Empirically, we observe that VNEstruct exhibits robustness on structural role identification tasks. Moreover, VNEstruct can achieve state-of-the-art performance on graph classification, without incorporating the graph structure information in the optimization, in contrast to GNN competitors.