# est.LG: Estimate graphons based on empirical degrees In graphon: A Collection of Graphon Estimation Methods

## 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

 1 est.LG(A, K)

## Arguments

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

\insertRef

Channarond2011graphon

\insertRef

chan2014graphon

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 ## Not run: ## generate a graphon of type No.10 with 3 clusters W = gmodel.preset(3,id=10) ## create a probability matrix for 100 nodes graphW = gmodel.block(W,n=100) P = graphW$P ## draw 23 observations from a given probability matrix A = gmodel.P(P,rep=23) ## run LG algorithm with a rough guess for K=2,3,4 res2 = est.LG(A,K=2) res3 = est.LG(A,K=3) res4 = est.LG(A,K=4) ## compare true probability matrix and estimated ones par(mfrow=c(1,4)) image(P); title("main") image(res2$P); title("LG with K=2") image(res3$P); title("LG with K=3") image(res4$P); title("LG with K=4") ## End(Not run)