Network Average Clustering Coefficient
The clustering coefficient for the whole network is given by Watts and Strogatz as the average of the local clustering coefficients of all the vertices :
A graph is considered small-world, if its average clustering coefficient is significantly higher than a random graph constructed on the same vertex set, and if the graph has approximately the same mean-shortest path length as its corresponding random graph.
A generalisation to weighted networks was proposed by Barrat et al. (2004), and a redefinition to bipartite graphs (also called two-mode networks) by Latapy et al. (2008) and Opsahl (2009).
This formula is not, by default, defined for graphs with isolated vertices; see Kaiser, (2008) and Barmpoutis et al. The networks with the largest possible average clustering coefficient are found to have a modular structure, and at the same time, they have the smallest possible average distance among the different nodes.
Read more about this topic: Clustering Coefficient
Famous quotes containing the words network and/or average:
“A culture may be conceived as a network of beliefs and purposes in which any string in the net pulls and is pulled by the others, thus perpetually changing the configuration of the whole. If the cultural element called morals takes on a new shape, we must ask what other strings have pulled it out of line. It cannot be one solitary string, nor even the strings nearby, for the network is three-dimensional at least.”
—Jacques Barzun (b. 1907)
“One cannot develop taste from what is of average quality but only from the very best.”
—Johann Wolfgang Von Goethe (1749–1832)