Secondly, we considered the network partitioning and we proposed a clustering method by reference to the stochastic matrix
using the MCL algorithm.
(II) We consider (1) with a well-known doubly stochastic matrix
which has applications in communication theory and graph theory .
For irreducible stochastic matrix
[M.sub.11], there exists a vector [mathematical expression not reproducible] with positive elements satisfying that [[beta].sup.T.sub.1][M.sub.11] = [[beta].sup.T.sub.1].
However, since n must also be a stochastic matrix
, the sum of its components must equal 1.
where p is the stationary probability vector of the irreducible stochastic matrix
A = [[summation].sup.N.sub.i=0] [A.sub.i] and [beta] = [[summation].sup.N.sub.i=0] [iA.sub.i]e.
Demetrius and Manke  propose the analysis of the stochastic matrix
in the context of network robustness.
However, there are some cases where [??] is a stochastic matrix
, even if it does not correspond to carries processes.
Let P be a stochastic matrix
defined on the countable state space G.
We refer to the index set of a stochastic matrix
as its state space.
Let S be a stochastic matrix
. If G(S) contains at least one spanning tree such that the root vertex of that spanning tree has a self-loop in G(S), then S is SIA.
[??] [there exists] 3 double stochastic matrix
P such that PXw = Xv we have another criterion for SSD relation:
Additionally, transition probability matrix P=[[p.sub.j]] has the property of a doubly stochastic matrix