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Component Evolution in General Random Intersection Graphs

  • Milan Bradonjić
  • Aric Hagberg
  • Nicolas W. Hengartner
  • Allon G. Percus
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6516)

Abstract

Random intersection graphs (RIGs) are an important random structure with algorithmic applications in social networks, epidemic networks, blog readership, and wireless sensor networks. RIGs can be interpreted as a model for large randomly formed non-metric data sets. We analyze the component evolution in general RIGs, giving conditions on the existence and uniqueness of the giant component. Our techniques generalize existing methods for analysis of component evolution: we analyze survival and extinction properties of a dependent, inhomogeneous Galton-Watson branching process on general RIGs. Our analysis relies on bounding the branching processes and inherits the fundamental concepts of the study of component evolution in Erdős-Rényi graphs. The major challenge comes from the underlying structure of RIGs, which involves both a set of nodes and a set of attributes, with different probabilities associated with each attribute.

Keywords

General random intersection graphs random graphs branching processes giant component stochastic processes in relation with random discrete structures 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Milan Bradonjić
    • 1
  • Aric Hagberg
    • 2
  • Nicolas W. Hengartner
    • 3
  • Allon G. Percus
    • 4
  1. 1.Theoretical Division and Center for Nonlinear StudiesLos Alamos National LaboratoryLos AlamosUSA
  2. 2.Theoretical DivisionLos Alamos National LaboratoryLos AlamosUSA
  3. 3.Information Sciences GroupLos Alamos National LaboratoryLos AlamosUSA
  4. 4.School of Mathematical SciencesClaremont Graduate UniversityClaremontUSA

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