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.

## See also

Spectral Coarse Graining
`scg-method`

,
`scg_eps()`

,
`scg_group()`

,
`scg_semi_proj()`

,
`scg()`

## 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] 0
```