sample_a_move_BetaSBM: Sampling a graph through a Markov move (basis) for beta-SBM

Description

sample_a_move_BetaSBM to sample a graph in the same fiber; sampling according to the beta-SBM (Karwa et al. (2023))

Usage

sample_a_move_BetaSBM(C, G_current)

Value

A graph

sampled graph: the sampled graph after one move as per the beta-SBM

Arguments

C: a positive integer vector of size n for block assignments of each node; from 1 to K (no of blocks)
G_current: an igraph object which is an undirected graph with no self loop

References

Karwa et al. (2023). "Monte Carlo goodness-of-fit tests for degree corrected and related stochastic blockmodels", Journal of the Royal Statistical Society Series B: Statistical Methodology, tools:::Rd_expr_doi("https://doi.org/10.1093/jrsssb/qkad084")

Examples

Run this code

RNGkind(sample.kind = "Rounding")
set.seed(1729)

# We model a network with 3 even classes
n1 = 5
n2 = 5
n3 = 5

# Generating block assignments for each of the nodes
n = n1 + n2 + n3
class = rep(c(1, 2, 3), c(n1, n2, n3))

# Generating the adjacency matrix of the network
# Generate the matrix of connection probabilities
cmat = matrix(
  c(
    10, 0.05, 0.05,
    0.05, 10, 0.05,
    0.05, 0.05, 10
  ),
  ncol = 3,
  byrow = TRUE
)
pmat = cmat / n

# Creating the n x n adjacency matrix
adj <- matrix(0, n, n)
for (i in 2:n) {
  for (j in 1:(i - 1)) {
    p = pmat[class[i], class[j]] # We find the probability of connection with the weights
    adj[i, j] = rbinom(1, 1, p) # We include the edge with probability p
  }
}

adjsymm = adj + t(adj)

# graph from the adjacency matrix
G = igraph::graph_from_adjacency_matrix(adjsymm, mode = "undirected", weighted = NULL)

# sampling a Markov move for the beta-SBM
G_sample = sample_a_move_BetaSBM(class, G)

# plotting the sampled graph
plot(G_sample, main = "The sampled graph after one Markov move for beta-SBM")