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
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