A framework to generate hypergraphs with community structure

TL;DR

This paper introduces a versatile framework for generating synthetic hypergraphs with community structures, enabling better evaluation and analysis of algorithms in systems with complex multi-body interactions.

Contribution

It presents a novel, flexible method for creating large hypergraphs with customizable community features, addressing a gap in synthetic hypergraph data generation.

Findings

Allows sampling hypergraphs with specific community structures

Enables analysis of community detection algorithms on synthetic data

Generates hypergraphs similar to real-world higher-order systems

Abstract

In recent years hypergraphs have emerged as a powerful tool to study systems with multi-body interactions which cannot be trivially reduced to pairs. While highly structured methods to generate synthetic data have proved fundamental for the standardized evaluation of algorithms and the statistical study of real-world networked data, these are scarcely available in the context of hypergraphs. Here we propose a flexible and efficient framework for the generation of hypergraphs with many nodes and large hyperedges, which allows specifying general community structures and tune different local statistics. We illustrate how to use our model to sample synthetic data with desired features (assortative or disassortative communities, mixed or hard community assignments, etc.), analyze community detection algorithms, and generate hypergraphs structurally similar to real-world data. Overcoming previous limitations on the generation of synthetic hypergraphs, our work constitutes a substantial advancement in the statistical modeling of higher-order systems.