Computing Motifs in Hypergraphs

Motifs are overrepresented and statistically significant sub-patterns in a network, whose identification is relevant to uncover its underlying functional units. Recently, its extraction has been performed on higher-order networks, but due to the complexity arising from polyadic interactions, and the similarity with known computationally hard problems, its practical application is limited. Our main contribution is a novel approach for hyper-subgraph census and higher-order motif discovery, allowing for motifs with sizes 3 or 4 to be found efficiently, in real-world scenarios. It is consistently an order of magnitude faster than a baseline state-of-art method, while using less memory and supporting a wider range of base algorithms.