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A random graph

Published online by Cambridge University Press:  14 July 2016

Sheldon M. Ross
Sheldon M. Ross*
Affiliation:
University of California, Berkeley
*
∗Postal address: Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720, U.S.A.
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Abstract

We consider an unordered graph where there is one arc emanating from each node. We suppose that the arc that emanates from i will go to j with probability Pj. The probability that the resultant graph is connected and a recursive formula for the distribution of the number of components it possesses are derived.

Keywords

RANDOM GRAPHCONNECTEDSCHUR CONVEX
Type
Short Communications
Information
Journal of Applied Probability , Volume 18 , Issue 1 , March 1981 , pp. 309 - 315
Copyright
Copyright © Applied Probability Trust 

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Footnotes

Research partially supported by the Air Force Office of Scientific Research (AFSC), USAF, under Grant AFOSR–77–3213B and the Office of Naval Research under Contract N00014–77–C–0299 with the University of California.

References

[1] Frank, H. and Frisch, I. (1971) Communication, Transmission and Transportation Networks. Addison-Wesley, Reading, Mass.Google Scholar
[2] Hardy, G. H., Littlewood, J. E. and Pólya, G. (1952) Inequalities. Cambridge University Press.Google Scholar
[3] Harris, B. (1960) Probability distributions related to random mappings. Ann. Math. Statist. 31, 1045–1062.Google Scholar
[4] Katz, I. (1955) Probability of indecomposability of a random mapping function. Ann. Math. Statist. 26, 512–517.Google Scholar
[5] Kruskal, M. D. (1954) The expected number of components under a random mapping function. Amer. Math. Monthly 61, 392–397.CrossRefGoogle Scholar