Figure 3.

(a,b) In the plane $\tau \in \mathrm{\{4.50,}\mathrm{4.55,}\dots ,\mathrm{5.45,}\mathrm{5.50\}}$ along the horizontal axis and random rewiring probability $p\in \mathrm{\{0,}\mathrm{1/30,}\dots ,\mathrm{29/30,}\mathrm{1\}}$ along the vertical axis. (a) Depicts the modularity index $Q$; (b) Depicts π, the maximum element of the PageRank vector normalised by its mean value. (c) For $\tau =5$, along the horizontal axis random rewiring probability $p\in \mathrm{\{0.400,}\mathrm{0.402,}\dots ,\mathrm{0.598,}\mathrm{0.600\}}$. Along the vertical axis are $Q$ the modularity index (left, blue), and $\pi$ the maximum element of PageRank vector normalised by its mean value (right, red). (d) Single trial. Example critical SWN. Adjacency matrix mapped to an $n$-by-$n$ grid where rows (and columns) represent vertices and white indicates the existence of an edge. Rows and columns of adjacency matrices have been permuted to visualise the modules, in accordance with²⁸. Pair $(\tau ,p\mathrm{)\; =\; (5,\; 0.522)}$.