netneurotools.metrics.diffusion_efficiency

netneurotools.metrics.diffusion_efficiency(W)

Calculate diffusion efficiency.

The diffusion efficiency between nodes i and j is the inverse of the mean first passage time from i to j, that is the expected number of steps it takes a random walker starting at node i to arrive for the first time at node j. Note that the mean first passage time is not a symmetric measure – mfpt(i,j) may be different from mfpt(j,i) – and the pair-wise diffusion efficiency matrix is hence also not symmetric.

This function is adapted and optimized from the Brain Connectivity Toolbox.

Warning

Test before use.

Parameters:

W ((N x N) ndarray) – Weighted/unweighted, direct/undirected connection weight/length array

Returns:

• GE_diff (float) – Global diffusion efficiency

• E_diff ((N x N) ndarray) – Pair-wise diffusion efficiency array

References

[1]

Goñi, J., Avena-Koenigsberger, A., Velez de Mendizabal, N., van den Heuvel, M. P., Betzel, R. F., & Sporns, O. (2013). Exploring the morphospace of communication efficiency in complex networks. PLoS One, 8(3), e58070.