# Exploring Community Structure

    library(nett)
    library(Matrix)

Let us create a simple degree-corrected planted parition (DCPP) model:

    set.seed(1)
    n = 1000 # the number of nodes
    Ktru = 4 # the number of true communties
    lambda = 15 # the average degree
    oir = 0.1 # the out-in ratio
    pri = rep(1,Ktru)/Ktru
    theta <- EnvStats::rpareto(n, 2/3, 3) # node conn. propensity parameter

    B = pp_conn(n, oir, lambda, pri, theta)$B  # create connectivity matrix
    z =  sample(Ktru, n, replace=T, prob=pri)  # sample node labels
    A = sample_dcsbm(z, B, theta) # sample the adjacency matrix

Check to see if the average degree matches the target:

    mean(rowSums(A))
    #> [1] 15.118

Compute and plot the community profile based on SNAC+ test statistic:

    tstat = snac_resample(A, nrep = 10, ncores = 1)
    #> Warning: did not converge in 10 iterations
    plot_smooth_profile(tstat, "A DCPP network")

See the article Adjusted chi-square test for degree-corrected block models, Zhang and Amini for how these profiles are constructed.