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

TL;DR

This paper introduces exact and sampling methods for efficiently identifying higher-order motifs in large hypergraphs, enabling faster analysis of complex systems with minimal accuracy loss.

Contribution

It presents novel algorithms that leverage hypergraph structures for faster motif counting and introduces sampling techniques for scalable motif estimation.

Findings

Exact methods outperform traditional techniques in speed

Sampling provides faster results with small estimation errors

Applicable to large real-world hypergraph datasets

Abstract

Network motifs are recurrent, small-scale patterns of interactions observed frequently in a system. They shed light on the interplay between the topology and the dynamics of complex networks across various domains. In this work, we focus on the problem of counting occurrences of small sub-hypergraph patterns in very large hypergraphs, where higher-order interactions connect arbitrary numbers of system units. We show how directly exploiting higher-order structures speeds up the counting process compared to traditional data mining techniques for exact motif discovery. Moreover, with hyperedge sampling, performance is further improved at the cost of small errors in the estimation of motif frequency. We evaluate our method on several real-world datasets describing face-to-face interactions, co-authorship and human communication. We show that our approximated algorithm allows us to extract higher-order motifs faster and on a larger scale, beyond the computational limits of an exact approach.