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