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## Chapter 14, Figure 5

Small world digraphs. (A) Analogous to the examples presented by Watts & Strogatz (1998), graphs are varied between totally regular (case a, "nearest neighbor") through intermediate cases (case b) to totally random (case c). A total of 256 connections are made between 32 vertices. Vertices are arranged in a circle (small blue circles) with red lines indicating bi-directional connections (edges), and green lines indicating unidirectional edges. A scatter plot of characteristic path length (lpath) and cluster index (fclust) is shown on the right. Numerous graphs exist for which the value of fclust is high, while the value of lpath is low. (B) Here, graphs are varied between "clustered" (case a) and totally random (case c). Compared to (A), higher cluster index values result for case a, as well as numerous intermediate cases. Note that, in both (A) and (B), characteristic path lengths are relatively short for almost all cases. This is due to the relatively high degree of connectivity (0.26), chosen to approximate that of cortical connection matrices. In Watts & Strogatz' original work, the degree of connectivity for typical small world examples was set to about 0.04 (n=1000, k=10 per vertex).

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