Some Distributions in the Theory of Graphs

  • Michael Capobianco
Part of the NATO Advanced study Institutes Series book series (ASIC, volume 79)


In certain types of populations, one is interested in the relationships among the individuals, e.g., animals and plants in a food web, persons in a social group, cities linked by various transportation routes, etc. These can be modeled by graphs or digraphs (directed graphs). Trying to infer something about these structures from a subgraph (sample) constitutes statistical inference in graphs (what we have called “stagra- phics”). There are many distributions which occur in graph theory which could be useful in inference. This paper is a survey of some of these distributions, specifically, degree distributions, path length distributions, distance distributions, cycle distributions, triad distributions, and distributions connected with pairs of stars. Various properties of these distributions will be discussed, as will their connections with inference. Several open problems will be presented.

Key words

graphs digraphs statistics distributions 


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Copyright information

© D. Reidel Publishing Company 1981

Authors and Affiliations

  • Michael Capobianco
    • 1
  1. 1.St. John’s UniversityStaten IslandUSA

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