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Network motifs are recurrent, small-scale patterns of interactions observedfrequently in a system. They shed light on the interplay between the topologyand the dynamics of complex networks across various domains. In this work, wefocus on the problem of counting occurrences of small sub-hypergraph patternsin very large hypergraphs, where higher-order interactions connect arbitrarynumbers of system units. We show how directly exploiting higher-orderstructures speeds up the counting process compared to traditional data miningtechniques for exact motif discovery. Moreover, with hyperedge sampling,performance is further improved at the cost of small errors in the estimationof motif frequency. We evaluate our method on several real-world datasetsdescribing face-to-face interactions, co-authorship and human communication. Weshow that our approximated algorithm allows us to extract higher-order motifsfaster and on a larger scale, beyond the computational limits of an exactapproach.

Exact and sampling methods for mining higher-order motifs in large hypergraphs