Diffusion probability matrix from transition matrix

Description here

get_diffusion_probability_matrix_from_T(Pi, tau)

get_diffu_Pt_from_T(Pi, tau)

get_diffu_Pt_from_Pi(Pi, tau)

get_diffusion_probability_matrix_from_Pi(Pi, tau)

Arguments

Pi

Transition matrix. We do not use T to avoid conflicts with the abbreviation for TRUE), instead we indicated the transition matrix with the capital greek letter \(\Pi\) in the equations and Pi in the code.

tau

diffusion time

Value

\(exp^{-\tau (I - \Pi)}\), exponential of the normalized Laplacian matrix corresponding to the given transition rate matrix (or transition probability matrix of a discrete-time Markov chain).

References

De Domenico, M. (2017). Diffusion Geometry Unravels the Emergence of Functional Clusters in Collective Phenomena. Physical Review Letters. doi:10.1103/PhysRevLett.118.168301

Bertagnolli, G., & De Domenico, M. (2020). Diffusion Geometry of Multiplex and Interdependent Systems. arxiv preprint arxiv:2006.13032

See also

get_diffusion_probability_matrix