# R igraph manual pages

Use this if you are using igraph from R

## 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 x n adjacency matrix with real non-negative entries. Let us define D=diag( sum(M[1,i], i), ..., sum(M[n,i], i) )

The (row) stochastic matrix is defined as

W = inv(D) 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 csardi.gabor@gmail.com

`as_adj`

### 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)

```

[Package igraph version 1.2.6 Index]