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:
“How have I been able to live so long outside Nature without identifying myself with it? Everything lives, moves, everything corresponds; the magnetic rays, emanating either from myself or from others, cross the limitless chain of created things unimpeded; it is a transparent network that covers the world, and its slender threads communicate themselves by degrees to the planets and stars. Captive now upon earth, I commune with the chorus of the stars who share in my joys and sorrows.”
—Gérard De Nerval (1808–1855)
“...you don’t have to be as good as white people, you have to be better or the best. When Negroes are average, they fail, unless they are very, very lucky. Now, if you’re average and white, honey, you can go far. Just look at Dan Quayle. If that boy was colored he’d be washing dishes somewhere.”
—Annie Elizabeth Delany (b. 1891)