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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×n adjacency matrix with real non-negative entries. Let us define D=diag(iM1i,,iMni)

The (row) stochastic matrix is defined as W=D1M, where it is assumed that D is non-singular. Column stochastic matrices are defined in a symmetric way.

See also

as_adj()

Spectral Coarse Graining scg-method

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