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.
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/directory: contains the Tags_ask_ubuntu dataset [1].Output/: Output of theTagsAskUbuntu_example.ipynbnotebook.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 `