Counting hypertriangles through hypergraph orientations

TL;DR

This paper introduces a new framework and algorithm for efficiently counting hypertriangles in hypergraphs, leveraging orientations and degeneracy concepts, with significant speed and memory improvements over existing methods.

Contribution

It generalizes classical graph algorithms to hypergraphs and provides the first provable, efficient hypertriangle counting algorithm with practical implementation.

Findings

DITCH is 10-100x faster than existing methods

DITCH uses less memory and is more scalable

The framework extends graph orientation techniques to hypergraphs

Abstract

Counting the number of small patterns is a central task in network analysis. While this problem is well studied for graphs, many real-world datasets are naturally modeled as hypergraphs, motivating the need for efficient hypergraph motif counting algorithms. In particular, we study the problem of counting hypertriangles - collections of three pairwise-intersecting hyperedges. These hypergraph patterns have a rich structure with multiple distinct intersection patterns unlike graph triangles. Inspired by classical graph algorithms based on orientations and degeneracy, we develop a theoretical framework that generalizes these concepts to hypergraphs and yields provable algorithms for hypertriangle counting. We implement these ideas in DITCH (Degeneracy Inspired Triangle Counter for Hypergraphs) and show experimentally that it is 10-100x faster and more memory efficient than existing state-of-the-art methods.