brainconn.clustering.transitivity_bd

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 matrix
Returns: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))