Random walk transition matrix for an edge-coloured network. Given the node tensor for the edge-coloured multi-layer network the function builds the supra transition matrix for a discrete time RW.

Source: R/muxLib_annotated.R

Random walk transition matrix for an edge-coloured network. Given the node tensor for the edge-coloured multi-layer network the function builds the supra transition matrix for a discrete time RW.

BuildTransitionMatrixFromEdgeColoredMatrices(
  NodesTensor,
  Layers,
  Nodes,
  Type = "classical"
)

Arguments

NodesTensor

list of adjacency matrices, expected to be aligned (a node has same index in any layer).
Layers

integer, number of layers
Nodes

integer, number of nodes
Type

the type of the random walk, default "classical". Other types: c("pagerank", "diffusive", "maxent"). For details on the transition rules see Refs.2-3.

Value

a square matrix of dimension Nodes of transition probabilities for a discrete-time random walk on the given edge-coloured network.

References

  1. De Domenico, M., Set al. (2013). Mathematical formulation of multilayer networks. Physical Review X, 3(4), 041022. doi 10.1103/PhysRevX.3.041022

  2. De Domenico, M., et al. (2014). Navigability of interconnected networks under random failures. PNAS, 111(23). doi 10.1073/pnas.1318469111

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