# stochastic_matrix

From igraph v1.0.0
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

```
library(Matrix)
## g is a large sparse graph
g <- barabasi.game(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 1.0.0, License: GPL (>= 2)*

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