Fig. 4: Average entropies of flower graphs—example.

We take N = 19 as an example. There are \(\left\lfloor (19+1)/2\right\rfloor =10\) extremal graphs; their plots of S^p versus p are shown in distinct colors. Each plot is characterized by a threshold value \(\tilde{p}\), which separates the linear and quadratic dependence of S^p in equation (20). Because the overall normalization of S^p is tunable, we display S^p of flower graphs a normalized to fix \({S}^{\left\lfloor (N+1)/2\right\rfloor }={S}^{10}\) and b normalized to fix S¹.