A First Course in Network Science by Filippo Menczer & Santo Fortunato & Clayton A. Davis

Author:Filippo Menczer & Santo Fortunato & Clayton A. Davis [Menczer, Filippo]
Language: eng
Format: azw3, epub
Publisher: Cambridge University Press
Published: 2020-02-05T16:00:00+00:00

Fig. 5.4 Small-world networks. (a) A hexagonal lattice, a graph where each node has six neighbors (except on the boundary). There are many triangles, so nodes have a high clustering coefficient. Paths from one corner to another have to traverse many links, therefore the average shortest-path length is large. (b) Four links have been rewired to randomly selected nodes, which are typically further away from the original endpoints. These links (in red) are shortcuts, and allow us to reach remote parts of the network via a low number of hops. For instance, the shortest path from the blue node to the green node goes from 10 steps on the lattice down to six steps through one of the shortcuts. Since only a few triangles are disrupted by the rewiring procedure, the clustering coefficient remains high.

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