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#### Keywords

Stochastic matrix; Stationary vector; Directed graph.

#### Abstract

Given a strongly connected directed graph D, let S_D denote the set of all stochastic matrices whose directed graph is a spanning subgraph of D. We consider the problem of completely describing the set of stationary vectors of irreducible members of S_D. Results from the area of convex polytopes and an association of each matrix with an undirected bipartite graph are used to derive conditions which must be satisfied by a positive probability vector x in order for it to be admissible as a stationary vector of some matrix in S_D. Given some admissible vector x, the set of matrices in S_D that possess x as a stationary vector is also characterised.

#### Recommended Citation

Breen, Jane and Kirkland, Steve.
(2015),
"Stationary vectors of stochastic matrices subject to combinatorial constraints",
*Electronic Journal of Linear Algebra*,
Volume 28.

DOI: http://dx.doi.org/10.13001/1081-3810.2988