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)
“... there is nothing more irritating to a feminist than the average “Woman’s Page” of a newspaper, with its out-dated assumption that all women have a common trade interest in the household arts, and a common leisure interest in clothes and the doings of “high society.” Women’s interests to-day are as wide as the world.”
—Crystal Eastman (1881–1928)