brainconn.clustering.clustering_coef_bd

clustering_coef_bd(A)

The clustering coefficient is the fraction of triangles around a node (equiv. the fraction of nodes neighbors that are neighbors of each other).

Parameters:A (NxN numpy.ndarray) – binary directed connection matrix Returns:C – clustering coefficient vector Return type:Nx1 numpy.ndarray

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))