Motif Prediction with Graph Neural Networks

Abstract

Link prediction is one of the central problems in graph mining. However, recent studies highlight the importance of higher-order network analysis, where complex structures called motifs are the first-class citizens. We first show that existing link prediction schemes fail to effectively predict motifs. To alleviate this, we establish a general motif prediction problem and we propose several heuristics that assess the chances for a specified motif to appear. To make the scores realistic, our heuristics consider -among others -correlations between links, i.e., the potential impact of some arriving links on the appearance of other links in a given motif. Finally, for highest accuracy, we develop a graph neural network (GNN) architecture for motif prediction. Our architecture offers vertex features and sampling schemes that capture the rich structural properties of motifs. While our heuristics are fast and do not need any training, GNNs ensure highest accuracy of predicting motifs, both for dense (e.g., k-cliques) and for sparse ones (e.g., k-stars). We consistently outperform the best available competitor by more than 10% on average and up to 32% in area under the curve. Importantly, the advantages of our approach over schemes based on uncorrelated link prediction increase with the increasing motif size and complexity. We also successfully apply our architecture for predicting more arbitrary clusters and communities, illustrating its potential for graph mining beyond motif analysis.

Equivariant and Stable Positional Encoding for More Powerful Graph Neural Networks

“…For example, for link prediction, GNN models, such as GCN (Kipf & Welling, 2017), GAE (Kipf & Welling, 2016) may perform even worse than some simple heuristics such as common neighbors and Adamic Adar (Liben-Nowell & Kleinberg, 2007) (see the performance comparison over the networks Collab and PPA in Open Graph Benchmark (OGB) (Hu et al, 2020)). Similar issues widely appear in node-set-based tasks such as network motif prediction (Liu et al, 2022;Besta et al, 2021), motif counting (Chen et al, 2020), relation prediction (Wang et al, 2021a;Teru et al, 2020) and temporal interaction prediction (Wang et al, 2021b), which posts a big concern for applying GNNs to these relevant real-world applications.…”