Exact and Sampling Methods for Mining Higher-Order Motifs in Large Hypergraphs
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Network motifs are patterns of interactions occurring among a small set of nodes in a graph. They highlight fundamental aspects of the interplay between the topology and the dynamics of complex networks and have a wide range of real-world applications. Motif analysis has been extended to a variety of network models that allow for a richer description of the interactions of a system, including weighted, temporal, multilayer, and, more recently, higher-order networks. Generalizing network motifs to capture patterns of group interactions is not only interesting from the fundamental perspective of understanding complex systems, but also proposes unprecedented computational challenges. In this work, we focus on the problem of counting occurrences of sub-hypergraph patterns in very large higher-order networks. We show that, by directly exploiting higher-order structures, we speed up the counting process compared to applying traditional data mining techniques for network motifs. Moreover, by including hyperedge sampling techniques, computational complexity is further reduced at the cost of small errors in the estimation of motif frequency. We evaluate our algorithms on several real-world datasets describing face-to-face interactions, co-authorship and human communication. We show that our approximated algorithm not only allows to speed up the performance, but also to extract larger higher-order motifs beyond the computational limits of an exact approach.
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