Toward a comprehensive simulation framework for hypergraphs: a Python-base approach

TL;DR

HyperRD delivers a Python-based, near-complete framework for representing, generating, analyzing, and simulating hypergraphs, addressing the lack of mature hypergraph toolchains. It combines two core modules for representation and analysis with random hypergraph generators and dynamics, and enables interoperability with NetworkX, HypernetX, and XGI. The authors implement two higher-order dynamics—Schelling-type segregation and a hypergraph SIR model—and illustrate their behavior on synthetic hypergraphs. By enabling higher-order interaction modeling in social and biological systems and promoting integration with existing Python ecosystems, HyperRD lowers barriers to interdisciplinary hypergraph research. Overall, the work provides a practical, extensible platform with potential for topology reconstruction, spectral analysis, and broader ML framework integration.

Abstract

Hypergraphs, or generalization of graphs such that edges can contain more than two nodes, have become increasingly prominent in understanding complex network analysis. Unlike graphs, hypergraphs have relatively few supporting platforms, and such dearth presents a barrier to more widespread adaptation of hypergraph computational toolboxes that could enable further research in several areas. Here, we introduce HyperRD, a Python package for hypergraph computation, simulation, and interoperability with other powerful Python packages in graph and hypergraph research. Then, we will introduce two models on hypergraph, the general Schelling's model and the SIR model, and simulate them with HyperRD.

Figures (3)

• Figure 1: HyperRD consists of two classes of main submodules. Two are for the representation of the hypergraph, and the others are for the analysis of hypergraphs. A hypergraph is constructed through the Create class and its containing features, as illustrated in this figure.
• Figure 2: In the implementation of the general Schelling's model, we consider a system consisting of 15 nodes distributed into three distinct labels, with each label assigned to 3 nodes. The initial configuration of these nodes is randomized. We ran the simulation of our model for 100 iterations. The initial state of the node configuration is depicted on the left side of the figure, while the right side illustrates the final state after 100 iterations. It is observed that nodes sharing identical labels tend to aggregate into a single hyperedge, demonstrating the model's inherent clustering dynamics.
• Figure 3: The SIR model on a hypergraph, designed for a maximum interaction order of 3 (3-hyperedges), is depicted for two distinct population sizes: 20 individuals (illustrated on the left) and 30 individuals (shown on the right). In this model, the hyperedges are constrained to a maximum order of 3. The parameters governing the model include a transmission rate $\beta$ set at 0.4 and a recovery rate $\gamma$ at 0.1. The simulation runs for 20 iterations/days.