A Survey on Hypergraph Mining: Patterns, Tools, and Generators

TL;DR

This survey comprehensively reviews hypergraph mining, including patterns, tools, and generators, highlighting current methods and future research directions in analyzing complex higher-order networks.

Contribution

It offers a detailed taxonomy and discussion of existing hypergraph mining tools, patterns, and generators, and outlines future research challenges.

Findings

Categorization of hypergraph mining tools into null models, structural elements, and structural quantities.

Overview of hypergraph generators for synthetic data creation.

Identification of open research challenges in hypergraph mining.

Abstract

Hypergraphs, which belong to the family of higher-order networks, are a natural and powerful choice for modeling group interactions in the real world. For example, when modeling collaboration networks, which may involve not just two but three or more people, the use of hypergraphs allows us to explore beyond pairwise (dyadic) patterns and capture groupwise (polyadic) patterns. The mathematical complexity of hypergraphs offers both opportunities and challenges for hypergraph mining. The goal of hypergraph mining is to find structural properties recurring in real-world hypergraphs across different domains, which we call patterns. To find patterns, we need tools. We divide hypergraph mining tools into three categories: (1) null models (which help test the significance of observed patterns), (2) structural elements (i.e., substructures in a hypergraph such as open and closed triangles), and (3) structural quantities (i.e., numerical tools for computing hypergraph patterns such as transitivity). There are also hypergraph generators, whose objective is to produce synthetic hypergraphs that are a faithful representation of real-world hypergraphs. In this survey, we provide a comprehensive overview of the current landscape of hypergraph mining, covering patterns, tools, and generators. We provide comprehensive taxonomies for each and offer in-depth discussions for future research on hypergraph mining.