Asymptotic distributions in random graphs with applications to social networks

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Abstract

Various kinds of subgraph counts have been proposed as important statistics in the social sciences: for instance, in connection with studies of the structural properties of social networks. Since the empirical structure in question often involves an element of randomness, subgraph counts are random variables and, consequently, we need to describe their probabilistic properties. In this paper we give a survey of results dealing with the asymptotic distributions of general subgraph counts for a number of standard graph distributions. Although we do not include proofs for all the results, we illustrate the methodology used through studies of asymptotic behaviour for certain subgraph counts.
Original languageEnglish
Pages (from-to)295-325
JournalStatistica Neerlandica
Volume45
Issue number3
DOIs
Publication statusPublished - 1991

Subject classification (UKÄ)

  • Probability Theory and Statistics

Keywords

  • orthogonal projection
  • uniform graphs
  • Bernoulli graphs
  • subgraph counts
  • induced subgraph counts

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