BlockModel.Gen {randnet}

Generates networks from degree corrected stochastic block model

Description

Generates networks from degree corrected stochastic block model, with various options for node degree distribution

Usage

BlockModel.Gen(lambda, n, beta = 0, K = 3, w = rep(1, K),
 Pi = rep(1, K)/K, rho = 0, simple = TRUE, power = TRUE,
alpha = 5, degree.seed = NULL)

Arguments

lambda

average node degree

n

size of network

beta

out-in ratio: the ratio of between-block edges over within-block edges

K

number of communities

w

not effective

Pi

a vector of community proportion

rho

proportion of small degrees within each community if the degrees are from two point mass disbribution. rho >0 gives degree corrected block model. If rho > 0 and simple=TRUE, then generate the degrees from two point mass distribution, with rho porition of 0.2 values and 1-rho proportion of 1 for degree parameters. If rho=0, generate from SBM.

simple

Indicator of wether two point mass degrees are used, if rho > 0. If rho=0, this is not effective

power

Whether or not use powerlaw distribution for degrees. If FALSE, generate from theta from U(0.2,1); if TRUE, generate theta from powerlaw. Only effective if rho >0, simple=FALSE.

alpha

Shape parameter for powerlaw distribution.

degree.seed

Can be a vector of a prespecified values for theta. Then the function will do sampling with replacement from the vector to generate theta. It can be used to control noise level between different configuration settings.

Value

A list of

A

the generated network adjacency matrix

g

community membership

P

probability matrix of the network

theta

node degree parameter

Author(s)

Tianxi Li, Elizaveta Levina, Ji Zhu
Maintainer: Tianxi Li [e-mail]

References

B. Karrer and M. E. Newman. Stochastic blockmodels and community structure in networks. Physical Review E, 83(1):016107, 2011.

A. A. Amini, A. Chen, P. J. Bickel, and E. Levina. Pseudo-likelihood methods for community detection in large sparse networks. The Annals of Statistics, 41(4):2097-2122, 2013.

T. Li, E. Levina, and J. Zhu. Network cross-validation by edge sampling. Biometrika, 107(2), pp.257-276, 2020.

Examples

dt <- BlockModel.Gen(30,300,K=3,beta=0.2,rho=0.9,simple=FALSE,power=TRUE)