For a given network size ($N=2$, 3, 4, 5, 6, 7), 6500 random networks were generated, but our completely random selection resulted in extreme values of heterogeneity that we considered as outliers. Thus, we estimated the CDF of the heterogeneity values using a kernel smoothing function (ksdensity in Matlab with bandwidth set to 0.1), and removed the top 1.5 percentile of points. There were at least $98.5%$ of points that remained (see Table 4 for the total number of points removed out of 6500).

Table 4:
After Estimating the CDF with Kernel Smoothing, the Total Number of Points Removed in the Tail Out of 6500 Random Samples Keeping the Lower 98.5 Percentile.
Heterogeneity \Network Size234567
$k$ 87 73 94 97 95 98
$h$ 96 96 94 91 95 93
$b$ 91 83 97 94 96 92
Heterogeneity \Network Size234567
$k$ 87 73 94 97 95 98
$h$ 96 96 94 91 95 93
$b$ 91 83 97 94 96 92

Note: Remaining heterogeneity values are in Figures 3, 4, and A2 to A7.

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