A simulated annealing algorithm for randomizing weighted networks

Scientific discovery in connectomics relies on the use of network null models. To systematically evaluate the prominence of brain network features, empirical measures are compared against null statistics computed in randomized networks. Modern imaging and tracing technologies provide an increasingly rich repertoire of biologically meaningful edge weights. Despite the prevalence of weighted graph analysis in connectomics, randomization models that only preserve binary node degree remain most widely used. Here, to adapt network null models to weighted network inference, we propose a simulated annealing procedure for generating strength sequence-preserving randomized networks. This model outperforms other commonly used rewiring algorithms in preserving weighted degree (strength). We show that these results generalize to directed networks as well as a wide range of real-world networks, making them generically applicable in neuroscience and in other scientific disciplines. Furthermore, we introduce morphospace representation as a tool for the assessment of null network ensemble variability and feature preservation. Finally, we show how the choice of a network null model can yield fundamentally different inferences about established organizational features of the brain such as the rich-club phenomenon and lay out best practices for the use of rewiring algorithms in brain network inference. Collectively, this work provides a simple but powerful inferential method to meet the challenges of analyzing richly detailed next-generation connectomics datasets.