Eigenvector-like centrality in non-uniform Hypergraphs

This repository contains the scripts, data and (pre-processed) figures from the : Uplifting edges in higher order networks: spectral centralities in non-uniform hypergraphs" paper by G. Contreras-Aso, C. Pérez-Corral, M. Romance, published in AIMS Mathematics and available as a preprint at arXiv:2310.20335.

Structure of the repository

The following files and directories are briefly summarized, in the same order as they appear within the paper.

• hyperfunctions.py: Our proposed measures and several auxiliary functions are defined here.
• other_measures.py: The vector centrality and the blowup uniformization (see paper for definitions), used for numerical comparisons, are defined here.
• Pairwise_comparisons.ipynb: Uplift from an example pairwise graph to a 3-uniform hypergraph whose HEC is calculated, and compared with the original EC.
• UPHEC_example.ipynb:: This notebook contains the computation of the UPHEC at each order on the toy model hypergraph, as well as the vector centrality on it.
• RankingAnalysis.ipynb: This notebook analyzes the output data from the previous notebook, in particular computing Kendall tau correlations between rankings.
• ZEC_example.ipynb: This notebook contains the computation of the Perron-like Z-eigenvector of an example hypergraph, following the example in the main text.
• Examples/: contains several notebooks and a subfolder
  • Examples/{hypergraph}_example.ipynb: These notebooks compute, for each hypergraph, all of the centralities (UPHEC, HEC, blowup uniformization) and saves them as a .csv file in the Output/ folder.
  • Examples/RankingAnalysis/{hypergraph)_RankingAnalysis.ipynb: This folder contains notebooks analyzing the already compued centralities for each hypergraph, generating the Kendall-tau plots to be save in Figures/.
• Output/: Output of the Examples/{hypergraph}_example.ipynb notebooks.
• Figures/: Pre-processed plots, saved from Examples/RankingAnalysis/{hypergraph)_RankingAnalysis.ipynb.

Data sources

All real hypergraphs are drawn from the XGI library [1] hypergraph database (XGI-DATA). There are some synthetic ones which we generate and analyze in the UPHEC_example.ipynb and ZEC_example.ipynb. Lastly, we also generate several random ones in Examples/random_example.ipynb with the xgi.generators.random.random_hypergraph() function.

[1] Landry, N. W., Lucas, M., Iacopini, I., Petri, G., Schwarze, A., Patania, A., & Torres, L. (2023). XGI: A Python package for higher-order interaction networks. Journal of Open Source Software, 8(85), 5162. https://doi.org/10.21105/joss.05162

How to cite

Bibtex citation:

@article{contreras2023uplifting,
  title = {Uplifting edges in higher-order networks: Spectral centralities for non-uniform hypergraphs},
  journal = {AIMS Mathematics},
  volume = {9},
  number = {11},
  pages = {32045-32075},
  year = {2024},
  issn = {2473-6988},
  doi = {10.3934/math.20241539},
  url = {https://www.aimspress.com/article/doi/10.3934/math.20241539},
  author = {Gonzalo Contreras-Aso and Cristian Pérez-Corral and Miguel Romance},
  keywords = {graph theory, hypergraphs, centrality, hypermatrices, eigenvectors},
}