Geodesic
Asymptotics of connectivity probabilities for pairs of graph nodes
Prikladnaya Diskretnaya Matematika. Supplement, no. 6 (2013), pp. 90-92

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For graphs with low reliable arcs, asymptotics of probabilities for connectivities between all pairs of nodes are constructed. Parameters of these asymptotics are characteristics of shortest paths in the graph. To calculate these characteristics, some modifications of classical algorithms are developed. On the base of these results, numerical experiment is realized. This experiment demonstrates advantages of suggested algorithms.
Keywords: shortest path, connectivity probability, computational complexity. 
@article{PDMA_2013_6_a43,
     author = {G. Sh. Tsitsiashvili and M. A. Osipova and A. S. Losev},
     title = {Asymptotics of  connectivity probabilities for pairs of graph nodes},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {90--92},
     publisher = {mathdoc},
     number = {6},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2013_6_a43/}
}
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G. Sh. Tsitsiashvili; M. A. Osipova; A. S. Losev. Asymptotics of  connectivity probabilities for pairs of graph nodes. Prikladnaya Diskretnaya Matematika. Supplement, no. 6 (2013), pp. 90-92. http://geodesic.mathdoc.fr/item/PDMA_2013_6_a43/