Fast degree-preserving rewiring of complex networks

In this paper we introduce a new, fast, degree-preserving rewiring algorithm for altering the assortativity of complex networks, which we call $\mathit{\text{Fast}}\mathit{\text{total}}\mathit{\text{link}}\mathit{\text{(FTL)}}\mathit{\text{rewiring}}$ 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 work we aim to overcome aforementioned scalability problems by performing a rewiring of all edges at once to achieve a very high assortativity 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 our proposed algorithm on networks with up to $100,000$ nodes and around $750,000$ edges and find that the relative improvements in speed remain, showing that the algorithm is both efficient and scalable.