Small World Graphs. Amber Rice. Defining a Small World Graph. Relatively HIGH Clustering Coefficient Relatively LOW Characteristic Path Length. Clustering Coefficient. Measure of degree to which vertices in a graph tend to cluster together
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Small World Graphs
8 Connected Triples
So the Clustering Coefficient is 3/8.
First, find the distances between all the vertices and each average length.
A – 1, 1, 2, 2 mean(A) = 6/4
B – 1, 1, 2, 2mean(B) = 6/4
C – 1, 1, 1, 1mean(C) = 4/4
D – 1, 2, 2, 2mean(D) = 7/4
E – 1, 2, 2, 2mean(E) = 7/4
Next, take the median of the averages.
Median ( 4/4, 6/4, 6/4, 7/4, 7/4 ) = 6/4
So, the Characteristic Path Length of this graph is 6/4.
Newman, M. E. J. (2003). The structure and function of complex networks. SIAM Review, 45(2):167-256.