compute.transition.matrix {RandomWalkRestartMH} | R Documentation

## Computes the transition matrix of a multiplex and heterogeneous network

### Description

`compute.transition.matrix` is a function to compute the transition matrix of a multiplex heterogeneous network provided as a `MultiplexHet` object.

### Usage

    compute.transition.matrix(x,lambda = 0.5, delta1=0.5, delta2=0.5)

### Arguments

`x` | A `MultiplexHet` object describing a multiplex and heterogeneous network generated by the function `create.multiplexHet`.
`lambda` | A numeric value between 0 and 1. It sets the probability of jumping within a network or change to the other network of the heterogeneous system. It is set by default to 0.5. See more details below.
`delta1` | A numeric value between 0 and 1. It sets the probability of performing inter-layer versus intra-layer transitions in the first multiplex. It is set by default to 0.5. See more details below.
`delta2` | A numeric value between 0 and 1. It sets the probability of performing inter-layer versus intra-layer transitions in the second multiplex. It is set by default to 0.5. See more details below.

### Details

We clarify the role of the different parameters in this point:

- `lambda`: For a given node, if a bipartite association exists, the particle can either jump between networks or stay in the current graph with a probability given by this parameter. The closer lambda is to one, the higher is the probability of jumping between networks following bipartite interactions.

- `delta`: This parameter sets the probability to change between layers at the next step. If delta = 0, the particle will always remain in the same layer after a non-restart iteration. On the other hand, if delta = 1, the particle will always change between layers, therefore not following the specific edges of each layer.

### Value

A square sparse transition matrix created with the `Matrix` package. It is the transition matrix for the Random Walk with Restart on Multiplex and Heterogeneous networks algorithm.

### Author(s)

Alberto Valdeolivas Urbelz alvaldeolivas@gmail.com

### See Also

`create.multiplexHet, compute.adjacency.matrix`

### Examples

    m1 <- igraph::graph(c(1,2,1,3,2,3), directed = FALSE)
    m2 <- igraph::graph(c(1,3,2,3,3,4,1,4), directed = FALSE)
    multiObject_1 <- create.multiplex(list(m1=m1,m2=m2))
    h1 <- igraph::graph(c("A","C","B","E","E","D","E","C"), directed = FALSE)
    bipartite_relations <- data.frame(m=c(1,3),h=c("A","E"))
    multiObject_2 <- create.multiplex(list(h1=h1))
    multiHetObject <- create.multiplexHet(multiObject_1, multiObject_2,
        bipartite_relations)
    compute.transition.matrix(multiHetObject)

[Package RandomWalkRestartMH version 1.14.0 Index]