Diffusion Probability Matrix

Source: R/get_diff_prob_matrix.R

Returns a matrix where each entry encodes the diffusion probability between two nodes

get_diffusion_probability_matrix(
  g,
  tau,
  type = "Normalized Laplacian",
  weights = NULL,
  verbose = TRUE
)

getDiffusionProbabilityMatrix(g, tau, type = "Normalized Laplacian", weights = NULL,
                                     verbose = TRUE)

get_diffu_Pt(
  g,
  tau,
  type = "Normalized Laplacian",
  weights = NULL,
  verbose = TRUE
)

Arguments

g

a single-layer network

tau

diffusion time

type

default "Normalized Laplacian". The type of Laplacian (i.e. of dynamics) to consider. Other types available are:

Laplacian

for the classical combinatorial Laplacian matrix; it governs the diffusion dynamics on the network

Normalized Laplacian

for the Laplacian matrix normalized by degree matrix, the so-called classical random walk normalized Laplacian; it governs stochastic walks on the network

Quantum Laplacian

for the Laplacian matrix normalized to be symmetric; it governs quantum walks on the network

MERW normalized Laplacian

the maximal-entropy random walk (RW) normalized Laplacian; it governs stochastic walks on the network, in which the random walker moves according to a maximal-entropy RW [1].

Note that you can type abbreviations, e.g. "L", "N", "Q", "M" for the respective types (case is ignored). The argument match is done through match_arg.

weights

edge weights, representing the strength/intensity (not the cost!) of each link. if weights is NULL (the default) and g has an edge attribute called weight, then it will be used automatically. If this is NA then no weights are used (even if the graph has a weight attribute).

verbose

default TRUE. If information on the type of Laplacian or on edge weights should be printed.

Value

The matrix \(exp^{-\tau L}\), exponential of a Laplacian matrix.

Functions

  • getDiffusionProbabilityMatrix(): Old deprecated function

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. (2021). Diffusion geometry of multiplex and interdependent systems. Physical Review E, 103(4), 042301. doi:10.1103/PhysRevE.103.042301 arXiv: 2006.13032