Stochastic matrix of a graph

Retrieves the stochastic matrix of a graph of class igraph.

Usage

stochastic_matrix(
  graph,
  column.wise = FALSE,
  sparse = igraph_opt("sparsematrices")
)

Arguments

graph

The input graph. Must be of class igraph.

column.wise

If FALSE, then the rows of the stochastic matrix sum up to one; otherwise it is the columns.

sparse

Logical scalar, whether to return a sparse matrix. The Matrix package is needed for sparse matrices.

Value

A regular matrix or a matrix of class Matrix if a sparse argument was TRUE.

Details

Let \(M\) be an \(n \times n\) adjacency matrix with real non-negative entries. Let us define \(D = \textrm{diag}(\sum_{i}M_{1i}, \dots, \sum_{i}M_{ni})\)

The (row) stochastic matrix is defined as $$W = D^{-1}M,$$ where it is assumed that \(D\) is non-singular. Column stochastic matrices are defined in a symmetric way.

See also

as_adjacency_matrix()

Author

Gabor Csardi csardi.gabor@gmail.com

Examples

library(Matrix)
## g is a large sparse graph
g <- sample_pa(n = 10^5, power = 2, directed = FALSE)
W <- stochastic_matrix(g, sparse = TRUE)

## a dense matrix here would probably not fit in the memory
class(W)
#> [1] "dgCMatrix"
#> attr(,"package")
#> [1] "Matrix"

## may not be exactly 1, due to numerical errors
max(abs(rowSums(W)) - 1)
#> [1] 5.651035e-13