Clustering coefficient C

clustering coefficient C is the average fraction of pairs of a person’s collaborators who have also collaborated with one another for a collaboration graph. Mathematically, $C={\frac {3\times number\ of\ triangles\ on\ the\ graph}{number\ of\ connected\ triples\ of\ vertices}}$.

Here a ‘‘triangle’’ is a trio of authors, each of whom is connected to both of the others, and a ‘‘connected triple’’ is a single author connected to two others. C = 1 for a fully connected graph and for a random graph, tends to zero as 1/N as the graph becomes large.