Geodesic
Nonnegative chainable matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXIII, Tome 496 (2020), pp. 5-25

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A description of nonnegative chainable matrices, based on fully indecomposable matrices, is given. The notion of the chainable rank of a nonnegative matrix is introduced and investigated. Properties of chainable matrices are used in studying stochastic Sarymsakov matrices. 
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     author = {Yu. A. Al'pin and I. V. Bashkin},
     title = {Nonnegative chainable matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--25},
     publisher = {mathdoc},
     volume = {496},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_496_a0/}
}
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Yu. A. Al'pin; I. V. Bashkin. Nonnegative chainable matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXIII, Tome 496 (2020), pp. 5-25. http://geodesic.mathdoc.fr/item/ZNSL_2020_496_a0/