Fast degree-preserving rewiring of complex networks

In this paper we introduce a new fast degree-preserving network rewiring algorithm. Commonly used existing algorithms require a large number of iterations, in particular in the case of large dense networks. This can especially be problematic when we wish to study ensembles of networks. In this paper we focus on degree assortative rewiring, and overcome aforementioned scalability problems by performing a rewiring of all edges at once to achieve a very high assorativity value before rewiring samples of edges at once to reduce this high assortativity value to the target value. The proposed method performs better than existing methods by several orders of magnitude for a range of structurally diverse complex networks, both in terms of the number of iterations taken, and time taken to reach a given assortativity value. Here we test networks up to ≈ 4,000 nodes and ≈ 88,000 edges and find that the relative improvements in speed remain.