Encyclopedia of Social Network Analysis and Mining

2018 Edition
| Editors: Reda Alhajj, Jon Rokne

Probabilistic Analysis

  • Robert R. SnappEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-7131-2_155



Asymptotically Almost Surely (a.a.s.)

The limit ℙ(En) → 1 as n → ∞, where {En} denotes a sequence of events defined on a random structure (e.g., a random graph) that depends on n


A subset of the sample space

\( \mathbb{G}\left(n,p\right) \)
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  1. Barrat A, Barthélemy M, Vespignani A (2008) Dynamical processes on complex networks. Cambridge University Press, CambridgezbMATHCrossRefGoogle Scholar
  2. Bearman PS, Moody J, Stovel K (2004) Chains of affection: the structure of adolescent romantic and sexual networks. Am J Sociol 110(1):44–91CrossRefGoogle Scholar
  3. Bollobás B (1985) Random graphs. Academic Press, LondonzbMATHGoogle Scholar
  4. Chernoff H (1952) A measure of asymptotic efficiency for test of a hypothesis base on a sum of observations. Ann Math Stat 23:493–507zbMATHCrossRefGoogle Scholar
  5. Durrett R (2007) Random graph dynamics. Cambridge University Press, CambridgezbMATHGoogle Scholar
  6. Erdős P, Rényi A (1959) On random graphs i. Publ Math Debr 6:290–297zbMATHGoogle Scholar
  7. Erdős P, Rényi A (1960) On the evolution of random graphs. Publ Math Inst Hung Acad Sci 5:17–61MathSciNetzbMATHGoogle Scholar
  8. Feller W (1968) An introduction to probability theory and its applications, vol I, 3rd edn. Wiley, New YorkzbMATHGoogle Scholar
  9. Gilbert EN (1959) Random graphs. Ann Math Stat 30:1141–1144zbMATHCrossRefGoogle Scholar
  10. Grimmett G, Stirzaker D (2001) Probability and random processes, 3rd edn. Oxford University Press, OxfordzbMATHGoogle Scholar
  11. Harris TE (1989) The theory of branching processes. Dover, MineolaGoogle Scholar
  12. Janson S, Łuczak T, Ruciński A (2000) Rańdom graphs. Wiley, New YorkzbMATHCrossRefGoogle Scholar
  13. Kolmogorov AN (1956) Foundations of probability, 2nd edn. Chelsea, New YorkzbMATHGoogle Scholar
  14. Lewin K (1997) Resolving social conflicts and field theory in social science. American Psychological Association, Washington, DCCrossRefGoogle Scholar
  15. Molloy M, Reed B (1995) A critical point for random graphs with a given degree sequence. Random Struct Algorithm 6(2–3):161–180MathSciNetzbMATHCrossRefGoogle Scholar
  16. Molloy M, Reed B (1998) The size of the giant component of a random graph with a given degree sequence. Comb Probab Comput 7(3):295–305MathSciNetzbMATHCrossRefGoogle Scholar
  17. Newman MEJ (2010) Networks: an introduction. Oxford University Press, OxfordzbMATHCrossRefGoogle Scholar
  18. Vega-Redondo F (2007) Complex social networks. Cambridge University Press, CambridgezbMATHCrossRefGoogle Scholar
  19. Venkatesh SS (2013) The theory of probability. Cambridge University Press, CambridgezbMATHGoogle Scholar
  20. Wilf HS (2006) Generatingfunctionology, 3rd edn. A K Peters, WellesleyzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of VermontBurlingtonUSA

Section editors and affiliations

  • Suheil Khoury
    • 1
  1. 1.American University of SharjahSharjahUnited Arab Emirates