igraph (version 0.6.6)

get.stochastic: Stochastic matrix of a graph

Description

Retrieves the stochastic matrix of a graph of class igraph.

Usage

get.stochastic(graph, column.wise = FALSE, sparse =
      getIgraphOpt("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.

Value

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

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

get.adjacency

Examples

library(Matrix)
## g is a large sparse graph
g <- barabasi.game(n = 10^5, power = 2, directed = FALSE)
W <- get.stochastic(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)

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