Steady and Ranging Persistence for Hypergraphs

Small piece of code in python to compute steady and ranging persistence of features of a hypergraph filtration.

Part of the code (mostly the file persistence.py) is borrowed from the following Generalized Persistence Analysis tool.

Dependencies

The code uses the following python module:

• sys, matplotlib, numpy, math, collections, colorsys;
• HyperNetX for hypergraph handling and visualization;
• tqdm for progress bar (optional).

Usage

In this repository, the tests are made with data derived from William Shakespeare’s plays. The data files are stored in the data/ folder and were taken from the Hyperbard dataset. Here is a great link for plenty of other hypergraph datasets.

To perform the test, go to the repository and call:

python3 test_hyperbard.py filename

with filename being a hyperbard edges.csv file, for instance:

python3 test_hyperbard.py data/king-lear_hg-scene-mw.edges.csv

First, the script will open the hyperbard file to build two hypergraph filtrations: the scene-hypergraph and the character-hypergraph filtrations of the play. The script will plot a sample of this two filtrations (for t=3,5,7,9).

Second, the script will compute four persistence diagrams for each filtrations:

• the steady persistence for the hyperhub feature;
• the ranging persistence for the hyperhub feature;
• the steady(=ranging) persistence for the exclusivity feature;
• the steady(=ranging) persistence for the max originality feature.

Example

Example of steady and ranging persistence for the scene-hypergraph filtration of King Lear: