Compute transition probabilities

Create a transition probability matrix from an adjacency matrix.

Usage

compute_transition_probabilities(A, k = 1, remove_self_loops = FALSE)

Arguments

A

An adjacency matrix

k

An integer value specifying the maximum steps from each node to expand the neighborhood. E.g. with k = 2, each node neighborhood will include the direct neighbors and nodes two steps away. With k = 1 (default), only the direct neighbors will be used.

remove_self_loops

Whether to remove self-loops from the transition probability matrix.

Value

A matrix of transition probabilities. The transition probability \(P^k(u \rightarrow v)\) for a k-step walk is found in row \(u\) and column \(v\) of the transition probability matrix. Row \(v\) and column \(u\) gives the reversed transition probability \(P^k(v \rightarrow u)\) for the k-step walk.

Examples

library(igraph)
#> 
#> Attaching package: ‘igraph’
#> The following object is masked from ‘package:Seurat’:
#> 
#>     components
#> The following object is masked from ‘package:tidygraph’:
#> 
#>     groups
#> The following objects are masked from ‘package:dplyr’:
#> 
#>     as_data_frame, groups, union
#> The following objects are masked from ‘package:stats’:
#> 
#>     decompose, spectrum
#> The following object is masked from ‘package:base’:
#> 
#>     union
g <- make_lattice(c(2, 3))
A <- as_adjacency_matrix(g)

# Transition probabilities
P_out <- compute_transition_probabilities(A)
P_out
#> 6 x 6 sparse Matrix of class "dgCMatrix"
#>                                                                 
#> [1,] .         0.5000000 0.5000000 .         .         .        
#> [2,] 0.5000000 .         .         0.5000000 .         .        
#> [3,] 0.3333333 .         .         0.3333333 0.3333333 .        
#> [4,] .         0.3333333 0.3333333 .         .         0.3333333
#> [5,] .         .         0.5000000 .         .         0.5000000
#> [6,] .         .         .         0.5000000 0.5000000 .