Encyclopedia of Social Network Analysis and Mining

Living Edition
| Editors: Reda Alhajj, Jon Rokne

Probabilistic Analysis

  • Robert R. Snapp
Living reference work entry
DOI: https://doi.org/10.1007/978-1-4614-7163-9_155-1



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

\( \mathbb{G}\left( n, p\right) \)


Random Graph Sample Space Simple Graph Probability Mass Function Mathematical Induction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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  1. Barrat A, Barthélemy M, Vespignani A (2008) Dynamical processes on complex networks. Cambridge University Press, CambridgeCrossRefzbMATHGoogle 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 23:493–507CrossRefzbMATHGoogle 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 30:1141–1144MathSciNetCrossRefzbMATHGoogle 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 YorkCrossRefzbMATHGoogle 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):161–180MathSciNetCrossRefzbMATHGoogle 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):295–305MathSciNetCrossRefzbMATHGoogle Scholar
  17. Newman MEJ (2010) Networks: an introduction. Oxford University Press, OxfordCrossRefzbMATHGoogle Scholar
  18. Vega-Redondo F (2007) Complex social networks. Cambridge University Press, CambridgeCrossRefzbMATHGoogle 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 2017

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