igraph (version 1.2.10)

stochastic_matrix: Stochastic matrix of a graph

Description

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 $D=\text{diag}(\sum _i{M}_{1i},\dots ,\sum _i{M}_{ni})$

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_adj

Examples

# NOT RUN {
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)

## may not be exactly 1, due to numerical errors
max(abs(rowSums(W))-1)

# }