I wanted to permute graph edges in a degree perserving manner for my analysis.
The problem is that the graph is very large so using a simple rewire algorithm is very slow (~230,000 edges, ~7,000 nodes).
I know that the original graph I am permutating is scale-free and the power law is that frequency of node connectivity k is 0.4412k^(-1.223). The graph is undirected, and all the nodes within it have at least degree 1 (the graph it taken from http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3214599/).
I thought of generating graphs with similar degree distribution using some algorithm for creating scale-free networks, and to assign afterwards the node labels from the original graph according to the rank of the degrees in a sorted list.
I saw that the R package igraph have a very fast implementation of Barabási algorithm. However, I do not know if I can parameterize it to produce a graph obeying my specific power law.