brainconn.clustering
.transitivity_bd¶
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transitivity_bd
(A)[source]¶ Transitivity is the ratio of ‘triangles to triplets’ in the network. (A classical version of the clustering coefficient).
Parameters: A (NxN numpy.ndarray
) – binary directed connection matrixReturns: T – transitivity scalar Return type: float Notes
Methodological note: In directed graphs, 3 nodes generate up to 8 triangles (2*2*2 edges). The number of existing triangles is the main
diagonal of S^3/2. The number of all (in or out) neighbour pairs is K(K-1)/2. Each neighbour pair may generate two triangles. “False pairs” are i<->j edge pairs (these do not generate triangles). The number of false pairs is the main diagonal of A^2. Thus the maximum possible number of triangles = (2 edges)*([ALL PAIRS] - [FALSE PAIRS])
= 2 * (K(K-1)/2 - diag(A^2)) = K(K-1) - 2(diag(A^2))