Link prediction is one of the central problems in graph mining. However, recent studies highlight the importance of the higher-order network analysis, where complex structures called motifs are the first-class citizens. We illustrate that existing link prediction schemes fail to predict the appearance of complex motifsin graph data. To address thisissue, we propose a general motif prediction problem . We establish the theoretical foundation of motif prediction and we propose several heuristics that , for a fixed set of nodes in a graph and a specified motif, assess the chances for this motif to appear. To make the scores realistic, our heuristics  - among others - consider correlations between links, i.e., the potential impact of some arriving links on the appearance of other parts of 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, using GNNs ensures highest accuracy when predicting the arrival of complex graph structures, both dense (e.g., k-cliques) and sparse (e.g., k-stars). Importantly, its advantages 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.
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.
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