Use this if you are using igraph from R
sample_correlated_gnp {igraph}  R Documentation 
Sample a new graph by perturbing the adjacency matrix of a given graph and shuffling its vertices.
sample_correlated_gnp(
old.graph,
corr,
p = edge_density(old.graph),
permutation = NULL
)
old.graph 
The original graph. 
corr 
A scalar in the unit interval, the target Pearson correlation between the adjacency matrices of the original and the generated graph (the adjacency matrix being used as a vector). 
p 
A numeric scalar, the probability of an edge between two vertices, it must in the open (0,1) interval. The default is the empirical edge density of the graph. If you are resampling an ErdosRenyi graph and you know the original edge probability of the ErdosRenyi model, you should supply that explicitly. 
permutation 
A numeric vector, a permutation vector that is
applied on the vertices of the first graph, to get the second graph. If

Please see the reference given below.
An unweighted graph of the same size as old.graph
such
that the correlation coefficient between the entries of the two
adjacency matrices is corr
. Note each pair of corresponding
matrix entries is a pair of correlated Bernoulli random variables.
Lyzinski, V., Fishkind, D. E., Priebe, C. E. (2013). Seeded graph matching for correlated ErdosRenyi graphs. https://arxiv.org/abs/1304.7844
sample_correlated_gnp_pair
,
sample_gnp
g < sample_gnp(1000, .1)
g2 < sample_correlated_gnp(g, corr = 0.5)
cor(as.vector(g[]), as.vector(g2[]))
g
g2