:pagefacingup: Paper | :paperclip: Docs | :computer: Tutorials | :floppy_disk: Data | :bug: Report bug

| :email: Reach us

HGX is a Python library for the analysis of real-world complex systems with group interactions and provides a comprehensive suite of tools and algorithms for constructing, visualizing, and analyzing hypergraphs.
The library is designed to be user-friendly and accessible, with a wide range of functionalities that can be applied to a diverse set of applications and use cases.

Disclaimer

• We welcome early feedback, discussions, ideas and contributions.

News

• 2023-03-28: HGX is now available!

Table of contents

• What are higher-order networks?
• What is hypergraphx?
• Library highlights
• Quick start
  • Installation
• Tutorials
• Data
• The HGX team
  • Project coordinators
  • Core members
  • Collaborators
• Contributing
• Citing HGX
• License
• Other resources

What are higher-order networks?

In the last few decades, networks have emerged as the natural tool to model a wide variety of natural, social and man-made systems. Networks, collections of nodes and links connecting pairs of them, are able to capture dyadic interactions only. However, in many real-world systems units interact in groups of three or more. Systems with non-dyadic interactions are ubiquitous, with examples ranging from cellular networks, drug recombination, structural and functional brain networks, human and animal face-to-face interactions, and collaboration networks. These higher-order interactions can be naturally described by alternative mathematical structures such as hypergraphs, where hyperedges connect groups of nodes of arbitrary size.

What is hypergraphx?

HGX aims to provide, as a single source, a comprehensive suite of tools and algorithms for constructing, storing, analysing and visualizing systems with higher-order interactions. 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, an implementation of different dynamical processes, from epidemics to diffusion and synchronization, with higher-order interactions, and more. Our computational framework is general, and allows to analyse hypergraphs with weighted, directed, signed, temporal and multiplex group interactions. Beyond experts in the field, we hope that our library will make higher-order network analysis accessible to everyone interested in exploring the higher-order dimension of relational data.

Library highlights

• HGX allows to store higher-order data as hypergraphs and to convert them to bipartite networks, maximal simplicial complexes, higher-order line graphs, dual hypergraphs, and clique-expansion graphs.
• It provides simple tools to characterize basic node and hyperedge statistics, such as hyperdegree distributions, correlations and assortativity, at the level of the whole higher-order network and of the individual nodes.
• Our library provides a variety of higher-order centrality measures for nodes and hyperedges, based on participation in different subhypergraphs, on spectral approaches, and on shortest paths and betweenness flows.
• HGX implements higher-order motif analysis. It also provides an approximated algorithm for motif analysis based on hyperedge sampling, able to speed up computations by orders of magnitudes with only a minimal compromise in accuracy.
• Our library provides spectral method to recover hard communities, generative models to extract overlapping communities and to infer hyperedges, methods to capture assortative and disassortative community structure and core-periphery organization in higher-order systems.
• We implement a variety of different tools to filter the most informative higher-order interactions, based on extracting statistically validated hypergraphs and identifying significant maximally interacting node groups.
• HGX offers a synthetic hypergraph samplers library, implementing various models such as Erdős-Rényi, scale-free, configuration and community-based models. It also includes a higher-order activity-driven model for temporal group interactions.
• We provide functions to simulate and analyze several dynamical process on higher-order networks, including synchronization, social contagion and random walks.
• HGX is highly flexible. It allows to store and analyze hypergraphs with a rich set of features associated with hyperedges, including interactions of different intensity, directions, sign, that vary in time or belong to different layers of a multiplex system.
• Our library provides different visualization tools to gain visual insights into the higher-order organization of real-world systems.

Quick start

Installation

pip install hypergraphx

or, if you really want the latest updates

pip install hypergraphx@git+https://github.com/HGX-Team/hypergraphx

Tutorials

You can find tutorials covering a variety of use cases here.

Data

Higher-order datasets are available in our data repository.

Citing HGX

If you use HGX or related data in your paper, please cite:

@article{lotito2023hypergraphx, author = {Lotito, Quintino Francesco and Contisciani, Martina and De Bacco, Caterina and Di Gaetano, Leonardo and Gallo, Luca and Montresor, Alberto and Musciotto, Federico and Ruggeri, Nicolò and Battiston, Federico}, title = "{Hypergraphx: a library for higher-order network analysis}", journal = {Journal of Complex Networks}, volume = {11}, number = {3}, year = {2023}, month = {05}, issn = {2051-1329}, doi = {10.1093/comnet/cnad019}, url = {https://doi.org/10.1093/comnet/cnad019}, note = {cnad019}, eprint = {https://academic.oup.com/comnet/article-pdf/11/3/cnad019/50461094/cnad019.pdf}, }

The HGX team

Project coordinators

• Quintino Francesco Lotito (lead developer) - quintino.lotito@unitn.it -
• Federico Battiston (project coordinator) - battistonf@ceu.edu

Core members

• Martina Contisciani - martina.contisciani@tuebingen.mpg.de
• Caterina De Bacco - caterina.debacco@tuebingen.mpg.de
• Leonardo Di Gaetano - leonardo.digaetano.96@gmail.com
• Luca Gallo - luca.gallo@uni-corvinus.hu -
• Alberto Montresor - alberto.montresor@unitn.it
• Federico Musciotto - federico.musciotto@unipa.it
• Nicolò Ruggeri - nicolo.ruggeri@tuebingen.mpg.de

Collaborators

• Lorenzo Betti
• Alberto Ceria
• Davide Colosimo
• Helcio Felippe
• Alec Kirkley
• Berné Nortier
• Alberto Vendramini

Contributing

HGX is a collaborative project and we welcome suggestions and contributions. If you are interested in contributing to HGX or have any questions about our project, please do not hesitate to reach out to us.

:running: I only have 1 minute

• Tweet about our library and spread the voice!
• Give the project a star on GitHub :star:!

:hourglassflowingsand: I've got 10 minutes

• Are you interested in higher-order motif analysis or community detection in hypergraphs? Try out our tutorials!
• Suggest ideas and engage in discussions
• Help someone with a problem
• Report a bug someone with a problem

:computer: I've got a few hours to work on this

• Create new tools for the community
• Help solving bugs reported in the issues
• Please read the more detailed contributing guidelines

:tada: I want to help grow the community

• Spread the voice!
• Talk about how HGX has been useful for your research problem
• Engage in a discussion with the core members of the library

License

Released under the 3-Clause BSD license ( see LICENSE.md)

HGX contains copied or modified code from third sources. The licenses of such code sources can be found in our license file

Other resources

Python

• ASH
• HyperNetX
• Reticula
• XGI

Julia

• HyperGraphs.jl
• SimpleHypergraphs.jl

R

• hyperG

Acknowledgments

This project is supported by the Air Force Office of Scientific Research under award number FA8655-22-1-7025.