# stochastic_matrix

From igraph v1.2.3
by Gabor Csardi

##### Stochastic matrix of a graph

Retrieves the stochastic matrix of a graph of class `igraph`

.

- Keywords
- graphs

##### 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`

.

##### See Also

##### 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)
# }
```

*Documentation reproduced from package igraph, version 1.2.3, License: GPL (>= 2)*

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