est.LG: Estimate graphons based on empirical degrees

Description

est.LG takes a 2-stage approach. First it adopts largest gap criterion on empirical degrees to estimate blocks of a given network under Stochastic Blockmodel framework. Then a consistent histogram estimator is utilized to estimate graphons based on estimated blocks in a given network.

Usage

est.LG(A, K = 2)

Arguments

an \((n\times n)\) binary adjacency matrix.

the number of blocks provided by an user.

Value

a named list containing

H: a \((K\times K)\) matrix of 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

Channarond2011graphon

chan2014graphon

Examples

Run this code

# NOT RUN {
## generate a graphon of type No.5 with 3 clusters
W = gmodel.preset(3,id=10)

## create a probability matrix for 20 nodes
graphW = gmodel.block(W,n=20)
P = graphW$P

## draw 23 observations from a given probability matrix
A = gmodel.P(P,rep=23,symmetric.out=TRUE)

## run LG algorithm with a rough guess for K=2,3,4
res2 = est.LG(A,K=2)
res3 = est.LG(A,K=3)
res4 = est.LG(A,K=4)

## compare true probability matrix and estimated ones
opar = par(no.readonly=TRUE)
par(mfrow=c(2,2), pty="s")
image(P, main="original P matrix")
image(res2$P, main="LG with K=2")
image(res3$P, main="LG with K=3")
image(res4$P, main="LG with K=4")
par(opar)

# }