On Local Aggregation in Heterophilic Graphs

TL;DR

This paper demonstrates that classical GNNs and MLPs can perform as well as or better than long-range aggregation methods on heterophilic graphs, and introduces the NIC metric as a better measure of local neighborhood information.

Contribution

It shows the effectiveness of classical GNNs and MLPs on heterophilic graphs and proposes the NIC metric as a more relevant measure of local information than homophily.

Findings

Classical GNNs match or outperform long-range methods on heterophilic graphs.

NIC correlates better with GNN accuracy than homophily.

Homophily is a poor indicator of local neighborhood information.

Abstract

Many recent works have studied the performance of Graph Neural Networks (GNNs) in the context of graph homophily - a label-dependent measure of connectivity. Traditional GNNs generate node embeddings by aggregating information from a node's neighbors in the graph. Recent results in node classification tasks show that this local aggregation approach performs poorly in graphs with low homophily (heterophilic graphs). Several mechanisms have been proposed to improve the accuracy of GNNs on such graphs by increasing the aggregation range of a GNN layer, either through multi-hop aggregation, or through long-range aggregation from distant nodes. In this paper, we show that properly tuned classical GNNs and multi-layer perceptrons match or exceed the accuracy of recent long-range aggregation methods on heterophilic graphs. Thus, our results highlight the need for alternative datasets to benchmark long-range GNN aggregation mechanisms. We also show that homophily is a poor measure of the information in a node's local neighborhood and propose the Neighborhood Information Content(NIC) metric, which is a novel information-theoretic graph metric. We argue that NIC is more relevant for local aggregation methods as used by GNNs. We show that, empirically, it correlates better with GNN accuracy in node classification tasks than homophily.