# ghypernet v1.0.0

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## Fit and Simulate Generalised Hypergeometric Ensembles of Graphs

Provides functions for model fitting and selection of generalised hypergeometric ensembles of random graphs (gHypEG). To learn how to use it, check the vignettes for a quick tutorial. Please reference its use as Casiraghi, G., Nanumyan, V. (2019) <doi:10.5281/zenodo.2555300> together with those relevant references from the one listed below. The package is based on the research developed at the Chair of Systems Design, ETH Zurich. Casiraghi, G., Nanumyan, V., Scholtes, I., Schweitzer, F. (2016) <arXiv:1607.02441>. Casiraghi, G., Nanumyan, V., Scholtes, I., Schweitzer, F. (2017) <doi:10.1007/978-3-319-67256-4_11>. Casiraghi, G., (2017) <arxiv:1702.02048> Casiraghi, G., Nanumyan, V. (2018) <arXiv:1810.06495>. Brandenberger, L., Casiraghi, G., Nanumyan, V., Schweitzer, F. (2019) <doi:10.1145/3341161.3342926> Casiraghi, G. (2019) <doi:10.1007/s41109-019-0241-1>.

# Introduction

ghypernet is an OpenSource R package that allows to estimate and work with Generalised Hypergeometric Ensembles of Random Graphs (gHypEG).

ghypernet has been developed specifically for the analysis of large networks characterised by a large number of repeated edges. It provides efficient methods to perform hypothesis testing and model selection on such data.

The theoretical foundation of this paper, gHypEGs, was developed in the following works:

1. Casiraghi, G., Nanumyan, V., Scholtes, I., Schweitzer, F. (2016) Generalized Hypergeometric Ensembles: Statistical Hypothesis Testing in Complex Networks. arXiv Prepr. arXiv1607.02441
2. Casiraghi, G., Nanumyan, V., Scholtes, I., Schweitzer, F. (2017) From Relational Data to Graphs: Inferring Significant Links Using Generalized Hypergeometric Ensembles in Social Informatics. SocInfo 2017 111-120 (Springer Verlag, 2017). doi:10.1007/978-3-319-67256-4_11
3. Casiraghi, G., Nanumyan, V. (2018) Generalised hypergeometric ensembles of random graphs: the configuration model as an urn problem. arXiv Prepr. arXiv1810.06495
4. Casiraghi, G. (2018) Analytical Formulation of the Block-Constrained Configuration Model. arXiv Prepr. arXiv1811.05337

# Dependencies

The package uses the library BiasedUrn to work with Wallenius' non-central hypergeometric distribution. Although this is not required, it is recommended to install the BiasedUrn R package, increasing the number of 'colors', i.e., the number of dimensions of the distribution. It can be easily done modifying the makevar file. In case the BiasedUrn library cannot be found, all computations will be performed using the multinomial approximation.

# Installation

You can install this package directly from GitHub. In R, run the following commands to install the package:

install.packages('devtools')
devtools::install_github("gi0na/r-ghypernet")

library(ghypernet)


# Acknowledgements

The research and development behind ghypernet is performed at the Chair of Systems Design, ETH Zürich.

# Contributors

Vahan Nanumyan

Laurence Brandenberger

ghypernet is licensed under the GNU Affero General Public License.