simu.SBM {changepoints}

Simulate a Stochastic Block Model (without change point).

Description

Simulate a Stochastic Block Model (without change point). The generated data is a matrix with each column corresponding to the vectorized adjacency (sub)matrix at a time point. For example, if the network matrix is required to be symmetric and without self-loop, only the strictly lower diagonal entries are considered.

Usage

simu.SBM(connec_mat, can_vec, n, symm = FALSE, self = TRUE)

Arguments

connec_mat

A numeric symmetric matrix representing the connectivity matrix (each entry takes value in [0,1]).

can_vec

A integer p-dim vector of node indices. can_vec is then divided into subvectors corresponding to blocks.

n

A integer scalar representing the number of observations.

symm

A logic scalar indicating if adjacency matrices are required to be symmetric.

self

A logic scalar indicating if adjacency matrices are required to have self-loop.

Value

A list with the following structure:

obs_mat

A matrix, with each column be the vectorized adjacency (sub)matrix. For example, if "symm = TRUE" and "self = FALSE", only the strictly lower triangular matrix is considered.

graphon_mat

Underlying graphon matrix.

Author(s)

Daren Wang & Haotian Xu

References

Wang, Yu and Rinaldo (2018) <arxiv:1809.09602>.

Examples

p = 15 # number of nodes
rho = 0.5 # sparsity parameter
block_num = 3 # number of groups for SBM
n = 100 # sample size for each segment
# connectivity matrix for the first and the third segments
conn1_mat = rho * matrix(c(0.6,1,0.6,1,0.6,0.5,0.6,0.5,0.6), nrow = 3) 
# connectivity matrix for the second segment
conn2_mat = rho * matrix(c(0.6,0.5,0.6,0.5,0.6,1,0.6,1,0.6), nrow = 3) 
set.seed(1)
can_vec = sample(1:p, replace = FALSE) # randomly assign nodes into groups
sbm1 = simu.SBM(conn1_mat, can_vec, n, symm = TRUE, self = TRUE)
sbm2 = simu.SBM(conn2_mat, can_vec, n, symm = TRUE, self = TRUE)
data_mat = cbind(sbm1$obs_mat, sbm2$obs_mat)