Geodesic
Asymptotics for connectivity probability of graph with low reliable arcs
Prikladnaâ diskretnaâ matematika, no. 1 (2013), pp. 93-98

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Asymptotics of connectivity probabilities for complete graphs with the low reliable arcs and for all pairs of nodes in them are constructed. Parameters of these asymptotics are characteristics of spanning trees and shortest paths. The calculation of the spanning trees characteristics is based on the Kirchhoff–Trent theorem. Modifications of classical algorithms are applied to calculate the characteristics of shortest paths.
Keywords: spanning tree, Kirchhoff's matrix, shortest path, connectivity probability, calculation complexity. 
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     author = {G. Sh. Tsitsiashvili and M. A. Osipova and A. S. Losev},
     title = {Asymptotics for connectivity probability of graph with low reliable arcs},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {93--98},
     publisher = {mathdoc},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2013_1_a7/}
}
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G. Sh. Tsitsiashvili; M. A. Osipova; A. S. Losev. Asymptotics for connectivity probability of graph with low reliable arcs. Prikladnaâ diskretnaâ matematika, no. 1 (2013), pp. 93-98. http://geodesic.mathdoc.fr/item/PDM_2013_1_a7/