This repository accompanies the article "The simpliciality of higher-order networks" by Nicholas Landry, Jean-Gabriel Young, and Nicole Eikmeier.

• The Data folder contains all of the global characteristics of the datasets (shown in Table 1 in the text), the Figures folder contains PDF and PNG files for each of the figures in the paper, and the tests folder contains unit tests to validate the code written for generating our results.
• The sod (Simpliciality of Data) folder contains all of the measures of simpliciality used in the paper as well as any utility functions.

• To run the unit tests and use the package, you need to pip install the package locally. Navigate to the local folder on your computer and run

pip install -e .

if you wish to be able to edit the distribution and

pip install .

if you don't.

• To run the unit tests, run pytest in the command line.
• The package is referenced as sod (Simpliciality of Data) when accessing the functionality.
• There are also distance versions of some simpliciality measures in the code.

Note: sod requires Python 3.10+!

• draw.py provides some additional functionality for drawing the multilayer hypergraph visualizations.
• empirical_simpliciality.py measures the simpliciality (all three measures) of the empirical datasets and stores the results in a JSON file in the Data folder.
• generate_dcsbm_parameters.py infers the parameters of the biSBM for a given empirical dataset for use in the model fitting script and stores as a JSON file in the Data folder.
• model_fitting.py generates realizations of the generative models, measures the resulting simpliciality, and then stores the results in a JSON file in the Data folder.
• simplicial_assortativity.py generates the empirical values of simplicial assortativity contained in Table 2.
• setup.py allows users to pip install this package.

• plot_empiricial_simpliciality.ipynb generates a plot of the simpliciality for empirical datasets, which is unused in the text. It also prints
• plot_model_fitting.ipynb generates Fig. 2 in the text.
• local_simpliciality.ipynb generates Fig. 3 in the text as well as corresponding local measures.
• dataset_characteristics.ipynb generates the results in Table 1 except the measures of simpliciality.
• illustrations.ipynb generates the diagrams used in Fig. 1 in the text.
• simpliciality_correlation.ipynb generates the correlation coefficients referenced in the text.
• cm_convergence.ipynb generates Fig. 4 in the text.
• print_simplicial_assortativity.ipynb prints the results from simplicial_assortativity.py as Table 2.