Accelerating Hypergraph Motif Counting Based on Hyperedge Relations.

Hypergraphs can naturally represent inter-group relations that are prevalent in many application domains by hyperedges. Hypergraph motifs can be described as the structural patterns of three connected hyperedges. As an effective tool, it plays an important role in the local structure analysis of hypergraphs. In this paper, we study exact hypergraph motif counting which is a fundamental problem of hypergraph motif research. Existing algorithms don’t adequately consider hyperedge relations in real-world hypergraphs, which lead to a large number of redundant computations. This motivates us to improve performance by exploiting hyperedge relations. In our work, we classify hypergraph motifs with different hyperedge relations. For different types of motifs, we use set theory to demonstrate and propose different optimization methods to reduce the computation of excessive intersections. We also further reduce the cost of the proposed method by preserving hyperedge intersections when constructing the hyperdege projected graph. Extensive experiments on real datasets validate the superiority of our algorithm compared to existing methods.