get_diffusion_probability_matrix_from_T: Diffusion probability matrix from transition matrix

In diffudist: Diffusion Distance for Complex Networks

Diffusion probability matrix from transition matrix

Description

Description here

Usage

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 Π in the equations and Pi in the code.
tau	diffusion time

Value

exp^{-τ (I - Π)}, 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

diffudist documentation built on March 7, 2023, 6:12 p.m.