Investigating GNN Convergence on Large Randomly Generated Graphs with Realistic Node Feature Correlations

TL;DR

This paper introduces a new method for generating large random graphs with correlated node features, revealing that GNN convergence behavior on realistic graphs may differ from previous studies, suggesting greater expressive power.

Contribution

The paper presents a novel graph generation technique with correlated features and provides theoretical and empirical analysis of GNN convergence on these graphs.

Findings

GNN convergence can be avoided on correlated graphs.

Correlated node features influence GNN expressive power.

Empirical validation shows divergence in GNN behavior on realistic graphs.

Abstract

There are a number of existing studies analysing the convergence behaviour of graph neural networks on large random graphs. Unfortunately, the majority of these studies do not model correlations between node features, which would naturally exist in a variety of real-life networks. Consequently, the derived limitations of GNNs, resulting from such convergence behaviour, is not truly reflective of the expressive power of GNNs when applied to realistic graphs. In this paper, we will introduce a novel method to generate random graphs that have correlated node features. The node features will be sampled in such a manner to ensure correlation between neighbouring nodes. As motivation for our choice of sampling scheme, we will appeal to properties exhibited by real-life graphs, particularly properties that are captured by the Barab\'asi-Albert model. A theoretical analysis will strongly indicate that convergence can be avoided in some cases, which we will empirically validate on large random graphs generated using our novel method. The observed divergent behaviour provides evidence that GNNs may be more expressive than initial studies would suggest, especially on realistic graphs.