Algorithm 1: Edge Rewiring to Adjust Assortativity 1 Select two blocks b$_{l}$ and b$_{l}$ ′ at random. 2 Select two edges ( N$_{1}$,N$_{2}$ ) and ( N$_{3}$,N$_{4}$ ) at random between blocks b$_{l}$ and b$_{l}$ ′ . 3 If | k$_{N}$$_{1}$ − k$_{N}$$_{2}$ | + | k$_{N}$$_{3}$ − k$_{N}$$_{4}$ | > | k$_{N}$$_{1}$ − k$_{N}$$_{4}$ | + | k$_{N}$$_{2}$ − k$_{N}$$_{3}$ | : Remove edges ( N$_{1}$,N$_{2}$ ) and ( N$_{3}$,N$_{4}$ ) Add edges ( N$_{1}$,N$_{4}$ ) and ( N$_{2}$,N$_{3}$ ) Figure 3: A schematic of degree assortative rewiring. Panel a displays a network, containing nodes N$_{1}$, ..., N$_{4}$ . Panel b highlights two edges selected within the same block pair. Panel c shows a potential rewiring, which will only occur if rewiring will increase assortativity. In this case, rewiring would increase degree assortativity, and panel d displays the rewiring. We are grateful for support from NIH Grants 2T32AI007358-26 and R37 AI51164. [1] Ove Frank and David Strauss. Markov graphs. Journal of the American Statistical Association , 81(395):832–842, 1986. References 17 Acknowledgements a b c d$^{N$_{1}$}$$^{N$_{3}$}$ N$_{2}$ N$_{4}$ N$_{1}$ N$_{3}$ N$_{2}$ N$_{4}$ N$_{1}$ N$_{3}$ N$_{2}$ N$_{4}$