Structural Patterns and Generative Models of Real-world Hypergraphs

TL;DR

This paper explores the structural patterns of real-world hypergraphs, introduces a multi-level decomposition method to analyze their properties, and proposes a simple generator model that replicates these properties effectively.

Contribution

It introduces a novel multi-level decomposition technique for hypergraphs and a simple generator model that captures key structural properties of real-world hypergraphs.

Findings

Hypergraphs obey five key structural properties at each decomposition level.

The proposed generator model successfully reproduces these properties.

The method provides a new foundation for hypergraph analysis and generation.

Abstract

Graphs have been utilized as a powerful tool to model pairwise relationships between people or objects. Such structure is a special type of a broader concept referred to as hypergraph, in which each hyperedge may consist of an arbitrary number of nodes, rather than just two. A large number of real-world datasets are of this form - for example, list of recipients of emails sent from an organization, users participating in a discussion thread or subject labels tagged in an online question. However, due to complex representations and lack of adequate tools, little attention has been paid to exploring the underlying patterns in these interactions. In this work, we empirically study a number of real-world hypergraph datasets across various domains. In order to enable thorough investigations, we introduce the multi-level decomposition method, which represents each hypergraph by a set of pairwise graphs. Each pairwise graph, which we refer to as a k-level decomposed graph, captures the interactions between pairs of subsets of k nodes. We empirically find that at each decomposition level, the investigated hypergraphs obey five structural properties. These properties serve as criteria for evaluating how realistic a hypergraph is, and establish a foundation for the hypergraph generation problem. We also propose a hypergraph generator that is remarkably simple but capable of fulfilling these evaluation metrics, which are hardly achieved by other baseline generator models.