On 05/25/2007 05:17 AM, Sven Teresniak wrote:
Hi,
what's the difference between
graph-tool --load z.dot \ --set-local-clustering-to-property=clustering \ --average-vertex-property="clustering|-"
and
graph-tool --load z.dot --global-clustering-coefficient=- ?
The results are not equal:
# average vertex property (clustering): 0.400881 0.001264
# global clustering coefficient: 0.016429 0.000001
But the global clustering coefficient IS the arithmetic mean of the local clustering coefficient of all edges, IIRC. I don't understand the divergence.
Hi.
The global clustering coefficient is defined differently as the mean of the local clustering coefficient. As stated in the documentation on the website, the global clustering is given by
C = 3 N_t / N_c, where N_t is the total number of closed triangles in the graph, and N_c is the number of triplets.
The average local clustering is C = \sum{C_i}/N, where C_i = 2N_c/(k(k-1)), where N is the total number of vertices, N_c is the number of connected neighbors, and k is the degree of the vertex.
Note that the above definitions are _not_ equivalent, and that's why you see the divergence.
Cheers.