Structure-Guided Input Graph for GNNs facing Heterophily

TL;DR

This paper tackles heterophily in graph neural networks by building structure-guided representations: it constructs two KNN graphs based on structural features ${\mathbf Z}_{\mathrm{role}}$ and ${\mathbf Z}_{\mathrm{global}}$, and uses an adaptive fusion mechanism to combine these with the original graph. The method introduces a multi-graph GNN (SG-GNN) that learns per-graph embeddings ${\mathbf Z}_i$ and fusion weights $\alpha_i$ with $\sum_i \alpha_i = 1$, optionally enabling node-specific coefficients $\boldsymbol{\alpha}_i$ so that each node selects the most informative graph. Experiments on six heterophilic datasets show that structure-based graphs are more homophilic (and thus better suited for low-pass GNNs), and that SG-GNN consistently outperforms the best single-input graph. The approach offers interpretable insights into which graph structure drives predictions and provides a flexible framework for robust node classification under heterophily. Key equations include $TV({\mathbf y}) = \| {\mathbf y} - {\mathbf A}{\mathbf y} \|_1$, $h_{edge} = \frac{|\{ (i,j) \in \mathcal{E} : y_i = y_j \}|}{|\mathcal{E}|}$, and per-node fusion constraints $\sum_i [\alpha_i]_n = 1$.

Abstract

Graph Neural Networks (GNNs) have emerged as a promising tool to handle data exhibiting an irregular structure. However, most GNN architectures perform well on homophilic datasets, where the labels of neighboring nodes are likely to be the same. In recent years, an increasing body of work has been devoted to the development of GNN architectures for heterophilic datasets, where labels do not exhibit this low-pass behavior. In this work, we create a new graph in which nodes are connected if they share structural characteristics, meaning a higher chance of sharing their labels, and then use this new graph in the GNN architecture. To do this, we compute the k-nearest neighbors graph according to distances between structural features, which are either (i) role-based, such as degree, or (ii) global, such as centrality measures. Experiments show that the labels are smoother in this newly defined graph and that the performance of GNN architectures improves when using this alternative structure.

Figures (4)

• Figure 1: Histograms for the node homophilies \ref{['eq:node_homoph']} for 4 graph datasets, as measured using the original graph from the dataset and our KNN graph using global structural features.
• Figure 2: Schema of the proposed architecture.
• Figure 3: Node classification accuracy using the original graph ${\mathcal{G}}$ and the proposed KNN graphs, ${\mathcal{G}}_{\text{feat}}$, ${\mathcal{G}}_{\text{role}}$, and ${\mathcal{G}}_{\text{global}}$. The numbers in the figure legends represent the number of neighbors $k$ used to create each KNN graph. Each boxplot is created for 10 different realizations of train-test splits.
• Figure 4: Heat maps of coefficients $\{\alpha_i\}$ learned from the proposed SG-GNN architecture.