A simulated annealing algorithm for randomizing weighted networks

Scientific discovery in connectomics relies on network null models. The prominence of network features is conventionally evaluated against null distributions estimated using randomized networks. Modern imaging technologies provide an increasingly rich array 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 we propose a simulated annealing procedure for generating randomized networks that preserve weighted degree (strength) sequences. We show that the procedure outperforms other rewiring algorithms and generalizes to multiple network formats, including directed and signed networks, as well as diverse real-world networks. Throughout, we use morphospace representation to assess the sampling behavior of the algorithm and the variability of the resulting ensemble. Finally, we show that accurate strength preservation yields different inferences about brain network organization. Collectively, this work provides a simple but powerful method to analyze richly detailed next-generation connectomics datasets. This study proposes an algorithm for generating randomized networks that preserve the weighted degree sequence. The procedure outperforms standard rewiring algorithms and extends to multiple network types, including directed and signed networks.