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, 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 alternative uniformization (see paper for definitions), used for 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.
• TagsAskUbuntu_example.ipynb: This notebook computes all of the centralities (UPHEC, HEC, Alternative uniformization) which will later be compared, on the Tags_ask_ubuntu dataset.
• 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.
• Dataset/: contains the Tags_ask_ubuntu dataset [1].
• Output/: Output of the TagsAskUbuntu_example.ipynb notebook.
• Figures/: Pre-processed plots.

[1] "Simplicial closure and higher-order link prediction". Austin R. Benson, Rediet Abebe, Michael T. Schaub, Ali Jadbabaie, and Jon Kleinberg. PNAS vol. 115, no. 48

Bibtex citation:

@article{contreras2023uplifting,
  title={Uplifting edges in higher order networks: spectral centralities for non-uniform hypergraphs},
  author={Contreras-Aso, Gonzalo and P{\'e}rez-Corral, Cristian and Romance, Miguel},
  journal={arXiv preprint arXiv:2310.20335},
  year={2023}
}