Fig. 1: Illustration of the population birth death process update rules and graph rewiring methods.

A illustrates both the dB (death-Birth) and the Bd (Birth-death) update rules. In (B), we use principle component analysis on 6 graph characteristics (mean, variance, third moment, modularity, average clustering, and assortativity) to highlight the network families studied, as well as the trajectories between them. Each graph family shows clustering using the first three principle components (that explain 89% of the variance in PC space). The black line represents the trajectory in PC space as we rewire graphs starting from preferential attachment (PA) graphs, through power law cluster networks (PLC) and uniform random geometric graphs, to normal random geometric graphs (RGG). C illustrates the edge swap operation used to tune graph characteristics. At first, there are no edges connecting nodes of degree 3 to nodes of degree 4. Two edges are randomly selected to be disconnected and nodes that were “parallel” with respect to the two disconnected edges are then connected, thus preserving the number of edges. After the rewiring step, there are two edges connecting nodes of degree 3 to nodes of degree 4, and there is no longer a 4-clique. The degrees of the nodes, however, are preserved.