C++ code for degree-preserving matrix rewiring (mex-wrapped for use in Matlab)
See https://github.com/artemyk/mexRewire for latest version.

Installation
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Download the code. Then, to build the mex file, change to the rewire_graph_mex directory and in MATLAB run:

make
Also make sure that the rewire_graph_mex directory is in your MATLAB path.

Usage
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This mex module provides a function to do degree-preserving rewiring a graph. It can be called by:

rewiredGraph = rewire_graph_cpp(G, num_of_rewires_per_edge [, constraintMatrix]);
Here, G is the graph to rewire, and num_of_rewires_per_edge is how many rewires per edge to carry out.

A matrix can be passed into the optional third parameter constraintMatrix if certain constraints should hold while rewiring. Specifically, if constraintMatrix is passed in, the rewiring code will only rewire an edge from i->j to k->l if and only if constraint_matrix(i,j) = constraint_matrix(k,l). So, for example, if constraint_matrix(i,j) contains the distance from i to j, edges will be rewired in a distance-preserving manner.

Notice that if the constraint matrix contains a continuous range of values, it may be impossible to find pairs (i,j) and (k,l) that both have the exact same values in the constraint matrix. In this case, the constraint can be 'softened' by first quantizing the constraint matrix to contain only one of several discrete values.

See rewire_example.m for a demonstration of use.