est.SBA: Estimate graphons based on Stochastic Blockmodel approximation

Description

est.SBA takes a 2-stage approach for estimating graphons based on exchangeable random graph models. First, it finds a Stochastic Blockmodel Approximation (SBA) of the graphon. Then, it uses clustering information to estimate graphon using a consistent histogram estimator.

Usage

est.SBA(A, delta = 0.5)

Arguments

either

Case 1.: an \((n\times n)\) binary adjacency matrix, or
Case 2.: a vector containing multiple of \((n\times n)\) binary adjacency matrices.

delta

a precision parameter larger than 0.

Value

a named list containing

H: a \((K\times K)\) matrix fo 3D histogram.
P: an \((n\times n)\) corresponding probability matrix.
B: a length-\(K\) list where each element is a vector of nodes/indices for each cluster.

References

Airoldi2013graphon

chan2014graphon

Examples

Run this code

# NOT RUN {
## generate a graphon of type No.6 with 3 clusters
W = gmodel.preset(3,id=6)

## create a probability matrix for 100 nodes
graphW = gmodel.block(W,n=100)
P = graphW$P

## draw 17 observations from a given probability matrix
A = gmodel.P(P,rep=17)

## run SBA algorithm with different deltas (0.2,0.5,0.8)
res2 = est.SBA(A,delta=0.2)
res3 = est.SBA(A,delta=0.5)
res4 = est.SBA(A,delta=0.8)

## compare true probability matrix and estimated ones
opar = par(no.readonly=TRUE)
par(mfrow=c(2,2), pty="s")
image(P); title("original P")
image(res2$P); title("SBA with delta=0.2")
image(res3$P); title("SBA with delta=0.5")
image(res4$P); title("SBA with delta=0.8")
par(opar)

# }