Effect of degree heterogeneity on state frequencies.

Panel A shows the degree statistics (mean and variance) for 1000 beta networks of size N = 200 for each α value shown. The mean connectivities were fixed at a value corresponding to p = 0.75 in the binomial random graph model. The axis label ‘B’ indicates a binomial random graph with N = 200 and p = 0.75; otherwise, the tick label indicates the value of α. The empirical mean degree is plotted in black (left axis) and the empirical degree variance in red (right axis). In each case, points mark the median ensemble value, and the vertical bars range from the first to third quartiles. The empirical degree variance was shifted slightly to the right to minimize overlap of the data. Panel B shows the frequency of each network state generated from the 1,000 beta networks for each α value, starting with random initial conditions. As α increases, the empirical degree variance decreases resulting in fewer temporally-irregular and more temporally-regular network states.