BlockModel.Gen: 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)

Value

A list of

A: the generated network adjacency matrix
g: community membership
P: probability matrix of the network
theta: node degree parameter

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.

Author

Tianxi Li, Elizaveta Levina, Ji Zhu
Maintainer: Tianxi Li tianxili@virginia.edu

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

Run this code


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

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