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nwlandry authored Mar 7, 2024
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# The simpliciality of higher-order networks

This repository accompanies the preprint, ["The simpliciality of higher-order networks"](https://doi.org/10.48550/arXiv.2308.13918) by Nicholas Landry, Jean-Gabriel Young, and Nicole Eikmeier.
This repository accompanies the article ["The simpliciality of higher-order networks"](https://doi.org/10.1140/epjds/s13688-024-00458-1) by Nicholas Landry, Jean-Gabriel Young, and Nicole Eikmeier.

### The structure of this repository is as follows:
* 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.
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* `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.

### Notebooks
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* `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.

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