Hypergraphx: a library for higher-order network analysis

Abstract

From social to biological systems, many real-world systems are characterized by higher-order, non-dyadic interactions. Such systems are conveniently described by hypergraphs, where hyperedges encode interactions among an arbitrary number of units. Here, we present an open-source python library, hypergraphx (HGX), providing a comprehensive collection of algorithms and functions for the analysis of higher-order networks. These include different ways to convert data across distinct higher-order representations, a large variety of measures of higher-order organization at the local and the mesoscale, statistical filters to sparsify higher-order data, a wide array of static and dynamic generative models, and an implementation of different dynamical processes with higher-order interactions. Our computational framework is general, and allows to analyse hypergraphs with weighted, directed, signed, temporal and multiplex group interactions. We provide visual insights on higher-order data through a variety of different visualization tools. We accompany our code with an extended higher-order data repository and demonstrate the ability of HGX to analyse real-world systems through a systematic analysis of a social network with higher-order interactions. The library is conceived as an evolving, community-based effort, which will further extend its functionalities over the years. Our software is available at https://github.com/HGX-Team/hypergraphx.

Legal hypergraphs

“…of variation in hypergraphs, researchers are increasingly adapting concepts and methods from topology to analyse higher-order network data [13,62,63], and they have also made some progress by leveraging (structurally more constrained) simplicial complexes [64][65][66][67]. Recent surveys have consolidated our knowledge of when and how to use higher-order network models or collected the mathematical and computational tools currently available for their study [9,[68][69][70][71], and the software landscape for working with higher-order network data has improved dramatically over the past few years [72][73][74]. Nevertheless, the study of higher-order network data is still in its relative infancy, especially when compared with traditional network analysis.…”

Not your private tête-à-tête: leveraging the power of higher-order networks to study animal communication

“…It includes tools for calculating descriptive measures, some basic generative models and visualization tools, alongside flexible core data structures for handling, converting, filtering and storing hypergraphs and simplicial complexes. Alternatives in Python also include HypergraphX [73], while scikit-TDA represents a more general collection of libraries for TDA [74]. In R , the tdaverse (https://github.com/tdaverse/tdaverse) provides tools for working with simplicial complexes, including plotting of Vietoris–Rips and Čech complexes, while the packages HyperG [75] and rhype [76] provide various algorithms for descriptive measures, basic generative models and plotting.…”

HyperNetX: A Python package for modeling complex network data as hypergraphs

“…Originally developed to efficiently discover spreading processes in complex social systems, the library now offers a statistics package as well as a full suite of hypergraph analysis and visualization tools (Landry et al, 2023). More recently, in 2023 HyperGraphX (HGX) was released, again with a full suite of tools for community detection as well as general hypergraph analytics (Lotito et al, 2023). A nice compendium of many of the hypergraph libraries created in the last decade can be found in Kurte et al (2021).…”