clustering coefficient

graph-tool
1

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.

CU
Sven

2

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.