Difference between revisions of "Clustering coefficient C"
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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. | 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, <math>C = \frac {3\times number\ of\ triangles\ on\ the\ graph}{number\ of\ connected\ triples\ of\ vertices}</math>. | Mathematically, <math>C = \frac {3\times number\ of\ triangles\ on\ the\ graph}{number\ of\ connected\ triples\ of\ vertices}</math>. | ||
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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. | 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. | ||
Latest revision as of 04:24, 4 February 2011
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, .
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.
