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

2024-01-16

arXiv.org

AI Summary

This work systematically investigates recurrent higher-order structural patterns across domains in hypergraphs and establishes an analytical framework capable of generating realistic synthetic hypergraphs. Method: We propose the first unified tripartite taxonomy for hypergraph mining—comprising pattern discovery, analytical tools, and generative models—integrating graph theory, random hypergraph models, statistical significance testing, and higher-order metrics (e.g., hypergraph transitivity). Our toolkit includes null models, substructure identification algorithms, and structural measures; we further design a feature-driven synthetic generator grounded in empirical hypergraph characteristics. Contribution/Results: We introduce the first multidimensional, fine-grained classification scheme and comprehensive research survey of hypergraph mining, explicitly identifying open challenges and interdisciplinary application pathways. This work lays a theoretical foundation and provides practical guidelines for higher-order network analysis, advancing both methodological rigor and real-world applicability in hypergraph science.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Bridging structured and unstructured data
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

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.

Problem

• Explore group interactions using hypergraph modeling.
• Identify recurring structural patterns in hypergraphs.
• Develop tools and generators for hypergraph mining.

Innovation

• Hypergraph modeling group interactions
• Null models for pattern significance
• Generators for synthetic hypergraphs