Figure 2 | Scientific Reports

Figure 2

From: Self-organisation of small-world networks by adaptive rewiring in response to graph diffusion

Figure 2

(a) Depicts the average π - maximum element of PageRank vector normalised by its mean - as a function of decreasing random rewiring probability \(p\in \mathrm{\{0,}\,\mathrm{1/30,}\,\ldots ,\,\mathrm{29/30,}\,\mathrm{1\}}\): Coloured lines indicate values of heat kernel parameter \(\tau \in \mathrm{\{0,}\,\varepsilon ,\,\mathrm{1,}\,\mathrm{8,}\,\delta \}\). (b) Depicts the bar-plot in which the height of individual bars is the average number of vertices having degree d v , where \({d}_{v}\le 20\). Inset bar-plot for vertex degrees d v , where 20 ≤ d v  ≤ 70. Probability density function (PDF) curves fitted to d v : truncated normal PDF for \(\tau \in \mathrm{\{0,}\,\varepsilon ,\,\mathrm{1\}}\) and truncated and normalised lognormal PDF for \(\tau \in \mathrm{\{8,}\,\delta \}\). Coloured bars (and curves) indicate values of heat kernel parameter \(\tau \); for each, \(p\) is chosen dependent on \(\tau \) such that S is at maximum. (c,d) Single trial. Example centralised 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) Depicts \((\tau ,\,p)\,=\,\mathrm{(8,\; 0.5667)}\); (d) depicts \((\tau ,\,p)=(\delta \mathrm{,\; 0.5667)}\).

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