stochastic_matrix: Stochastic matrix of a graph

In igraph: Network Analysis and Visualization

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.

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.

Value

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

Author(s)

Gabor Csardi [e-mail]

See Also

as_adjacency_matrix()

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)

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

igraph documentation built on Oct. 20, 2024, 1:06 a.m.