stochastic_matrix {igraph}  R Documentation 
Retrieves the stochastic matrix of a graph of class igraph
.
stochastic_matrix(
graph,
column.wise = FALSE,
sparse = igraph_opt("sparsematrices")
)
graph 
The input graph. Must be of class 
column.wise 
If 
sparse 
Logical scalar, whether to return a sparse matrix. The

Let M
be an n \times n
adjacency matrix with real
nonnegative 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 nonsingular. Column stochastic
matrices are defined in a symmetric way.
A regular matrix or a matrix of class Matrix
if a
sparse
argument was TRUE
.
Gabor Csardi csardi.gabor@gmail.com
Spectral Coarse Graining
scgmethod
,
scg_eps()
,
scg_group()
,
scg_semi_proj()
,
scg()
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)