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>.

Readme

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:

Casiraghi, G., Nanumyan, V., Scholtes, I., Schweitzer, F. (2016) Generalized Hypergeometric Ensembles: Statistical Hypothesis Testing in Complex Networks. arXiv Prepr. arXiv1607.02441
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
Casiraghi, G., Nanumyan, V. (2018) Generalised hypergeometric ensembles of random graphs: the configuration model as an urn problem. arXiv Prepr. arXiv1810.06495
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

Giona Casiraghi (project lead)

Vahan Nanumyan

Laurence Brandenberger

Copyright

ghypernet is licensed under the GNU Affero General Public License.

Functions in ghypernet

Name	Description
RMSLE	Computes the Root Mean Squared Logged Error
adj2el	Maps adjacency matrix to edgelist
bccm	Fitting bccm models
as.ghype	Map list to ghype object
adj_karate	Zachary's Karate Club graph
coef.nrm	Extraction method for coefficients of models of class 'nrm'.
BootstrapProperty	BootstrapProperty computes igraph analytics function on ensemble
ghype	Fitting gHypEG models
conf.test	Test regular (gnp) vs configuration model
dtcommittee	Swiss MPs committee affiliation data frame.
JnBlock	Fisher Information matrix for estimators in block models.
RMSE	Computes the Root Mean Squared Error
contacts.adj	Highschool contact network adjacency matrix
checkGraphtype	Check graph input type (for whether it's a graph or a edgelist).
gof.test	Perform a goodness-of-fit test
highschool.multiplex	Highschool contact network multiplex representation
nrmChoose	Selects the best set of predictors among the given sets by means of AIC.
nrm_selection	Perform AIC forward selection for nrm.
highschool.predictors	Highschool contact network predictors
loglratio	Compute log-likelihood ratio for ghype models.
logl	General method to compute log-likelihood for ghype models.
el2adj	Maps edgelist to adjacency matrix
reciprocity_stat	Calculate weighted reciprocity change statistics for multi-edge graphs.
cospons_mat	Swiss MPs network adjacency matrix
mcfaddenR2	Computes Mc Fadden pseudo R-squared.
homophily_stat	Calculate homophily in multi-edge graphs.
residuals.nrm	Method to compute residuals of nrm models
mat2vec.ix	Auxiliary function, gives mask for matrix for directed, undirected etc.
lr.test	Perform likelihood ratio test between two ghype models.
ComputeXi	Auxiliary function. Computes combinatorial matrix.
isNetwork	Test null model vs full ghype.
coxsnellR2	Computes Cox and Snell pseudo R-squared for nrm models.
rghype	Generate random realisations from ghype model.
createPredictors	Create a nrmpredictor object from passed argument
regularm	Fit the gnm model
linkSignificance	Estimate statistical deviations from ghype model
summary.nrm_selection	Summary method for elements of class 'nrm_selection'.
nr.ci	Confidence intervals for nrm models.
summary.nrm	Summary method for elements of class 'nrm'.
logLik.ghype	Extract Log-Likelihood
nr.significance	Computes the significance of more complex model against a simpler model by means of a likelihood ratio test.
nrm	Fitting gHypEG regression models for multi-edge networks.
CreateIgGraphs	Convert a list of adjacency matrices to a list of igraph graphs.
FitOmega	Fit propensity matrix for full model
scm	Fit the Soft-Configuration Model
sharedPartner_stat	Calculate (un-)weighted shared partner change statistics for multi-edge graphs.
createPredictors.list	Create a nrmpredictor object from list
vec2mat	Auxiliary function, produces matrix from vector
dt	Swiss MPs attribute data frame.
predict.nrm	Method to predict the expected values of a nrm model
onlinesim_mat	Swiss MPs committee similarity matrix.
vertexlabels	Zachary's Karate Club vertex faction assignment
No Results!

Name

Description

RMSLE

Computes the Root Mean Squared Logged Error

adj2el

Maps adjacency matrix to edgelist

bccm

Fitting bccm models

as.ghype

Map list to ghype object

adj_karate

Zachary's Karate Club graph

coef.nrm

Extraction method for coefficients of models of class 'nrm'.

BootstrapProperty

BootstrapProperty computes igraph analytics function on ensemble

ghype

Fitting gHypEG models

conf.test

Test regular (gnp) vs configuration model

dtcommittee

Swiss MPs committee affiliation data frame.

JnBlock

Fisher Information matrix for estimators in block models.

RMSE

Computes the Root Mean Squared Error

contacts.adj

Highschool contact network adjacency matrix

checkGraphtype

Check graph input type (for whether it's a graph or a edgelist).

gof.test

Perform a goodness-of-fit test

highschool.multiplex

Highschool contact network multiplex representation

nrmChoose

Selects the best set of predictors among the given sets by means of AIC.

nrm_selection

Perform AIC forward selection for nrm.

highschool.predictors

Highschool contact network predictors

loglratio

Compute log-likelihood ratio for ghype models.

logl

General method to compute log-likelihood for ghype models.

el2adj

Maps edgelist to adjacency matrix

reciprocity_stat

Calculate weighted reciprocity change statistics for multi-edge graphs.

cospons_mat

Swiss MPs network adjacency matrix

mcfaddenR2

Computes Mc Fadden pseudo R-squared.

homophily_stat

Calculate homophily in multi-edge graphs.

residuals.nrm

Method to compute residuals of nrm models

mat2vec.ix

Auxiliary function, gives mask for matrix for directed, undirected etc.

lr.test

Perform likelihood ratio test between two ghype models.

ComputeXi

Auxiliary function. Computes combinatorial matrix.

isNetwork

Test null model vs full ghype.

coxsnellR2

Computes Cox and Snell pseudo R-squared for nrm models.

rghype

Generate random realisations from ghype model.

createPredictors

Create a nrmpredictor object from passed argument

regularm

Fit the gnm model

linkSignificance

Estimate statistical deviations from ghype model

summary.nrm_selection

Summary method for elements of class 'nrm_selection'.

nr.ci

Confidence intervals for nrm models.

summary.nrm

Summary method for elements of class 'nrm'.

logLik.ghype

Extract Log-Likelihood

nr.significance

Computes the significance of more complex model against a simpler model by means of a likelihood ratio test.

nrm

Fitting gHypEG regression models for multi-edge networks.

CreateIgGraphs

Convert a list of adjacency matrices to a list of igraph graphs.

FitOmega

Fit propensity matrix for full model

scm

Fit the Soft-Configuration Model

sharedPartner_stat

Calculate (un-)weighted shared partner change statistics for multi-edge graphs.

createPredictors.list

Create a nrmpredictor object from list

vec2mat

Auxiliary function, produces matrix from vector

Swiss MPs attribute data frame.

predict.nrm

Method to predict the expected values of a nrm model

onlinesim_mat

Swiss MPs committee similarity matrix.

vertexlabels

Zachary's Karate Club vertex faction assignment

No Results!

Vignettes of ghypernet

Name
images/tikz_nweffects.pdf
Significantlinks.Rmd
Tutorial_NRM.Rmd
bibliography.bib
tutorial.Rmd
No Results!

Name

images/tikz_nweffects.pdf