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:
“Of what use, however, is a general certainty that an insect will not walk with his head hindmost, when what you need to know is the play of inward stimulus that sends him hither and thither in a network of possible paths?”
—George Eliot [Mary Ann (or Marian)
“The average Kentuckian may appear a bit confused in his knowledge of history, but he is firmly certain about current politics. Kentucky cannot claim first place in political importance, but it tops the list in its keen enjoyment of politics for its own sake. It takes the average Kentuckian only a matter of moments to dispose of the weather and personal helath, but he never tires of a political discussion.”
—For the State of Kentucky, U.S. public relief program (1935-1943)