Description Usage Arguments Value References See Also Examples
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.
1 | est.LG(A, K = 2)
|
A |
an (n\times n) binary adjacency matrix. |
K |
the number of blocks provided by an user. |
a named list containing
a (K\times K) matrix of 3D histogram.
an (n\times n) corresponding probability matrix.
a length-K list where each element is a vector of nodes/indices for each cluster.
Channarond2011graphon
\insertRefchan2014graphon
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | ## 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)
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