Figure 1.

(a) Depicts the small-world index S as a function of decreasing random rewiring probability p ∈ {0, 1/30, …, 29/30, 1}: Coloured lines indicate values of heat kernel parameter $\tau \in \mathrm{\{0,}\epsilon ,\mathrm{1,}\mathrm{8,}\delta \}$,  black line indicates the Watts-Strogatz algorithm with random rewiring probability $p\in \mathrm{\{0,}\mathrm{1/500,}\dots ,\mathrm{499/500,}\mathrm{1\}}$. (b) Depicts the average modularity Q as a function of decreasing random rewiring probability $p\in \mathrm{\{0,}\mathrm{1/30,}\dots ,\mathrm{29/30,}\mathrm{1\}}$: Coloured lines indicate values of heat kernel parameter $\tau \in \mathrm{\{0,}\epsilon ,\mathrm{1,}\mathrm{8,}\delta \}$. (c,d) Single trial. Example modular SWN. Adjacency matrices 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. (c) $(\tau ,p)=(\epsilon ,\mathrm{0.1)}$; (d) $(\tau ,p)=\mathrm{(1,}\mathrm{0.3)}$.