A Centrality Measure Using Magnitude Homology

This repository provides code to compute the (Eulerian) magnitude homology with $\mathbb{F}_2$ coefficients and in particular also implements the (Eulerian) magnitude homology centrality.

Dependencies

To run the code, install the neccessairy packages with conda env create --file environment.yml and activate the environment with conda activate mh_cent and use the environment to execute the notebooks.

Computing (Eulerian) magnitude homology centrality

In the notebook playground.ipynb you can find an example on how to get the betti numbers of (Eulerian) magnitude homology for a graph.

Running experiments

Axioms of Centrality Measures

The empirical validation of the different axioms can be found in the notebook axioms.ipynb.

Comparison to Existing Centrality Measures

For creating the figures of the different centrality measures and correlations on individual graphs, run the notebook centrality_plots.ipynb.

To run the experiment of computing the pearson correlation coefficients on the Netzschleuder catalogue, run python -m scripts.correlation For the variation of predicting the centrality from another centrality measure from linear regression over nodes from different graphs, run python -m scripts.cent_linreg To generate the heatmaps run the notebook correlation.ipynb.