# stochastic matrix

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## stochastic matrix

[stō′kas·tik ′mā·triks]
(mathematics)
A square matrix with nonnegative real entries such that the sum of the entries of each row is equal to 1.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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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 [15].
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 [31] 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.
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.
Additionally, transition probability matrix P=[[p.sub.j]] has the property of a doubly stochastic matrix since:

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