# compute.transition.matrix: Computes the transition matrix of a multiplex and... In RandomWalkRestartMH: Random walk with restart on multiplex and heterogeneous Networks

## Description

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

## Usage

 `1` ```compute.transition.matrix(x,lambda = 0.5, delta=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. `delta` A numeric value between 0 and 1. It sets the probability of performing inter-layer versus intra-layer transitions. 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

```create.multiplexHet, compute.adjacency.matrix```
 ```1 2 3 4 5 6 7 8``` ```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 <- create.multiplex(m1,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")) multiHetObject <- create.multiplexHet(multiObject, h1,bipartite_relations) compute.transition.matrix(multiHetObject) ```