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1 results

  • 7 - Small Subgraphs

  • from Part II - Erdős–Rényi–Gilbert Model
  • Alan Frieze, Carnegie Mellon University, Pennsylvania, Michał Karoński, Adam Mickiewicz University, Poznań, Poland
  • Book:
    Random Graphs and Networks: A First Course
    Published online:
    02 March 2023
    Print publication:
    09 March 2023, pp 85-92

  • Summary

    In this chapter, we see how many random edges are required to have a particular fixed size subgraph w.h.p. In addition, we will consider the distribution of the number of copies of strictly balanced subgraphs. From these general results, one can deduce thresholds for small trees, stars, cliques, bipartite cliques, and many other small subgraphs which play an important role in the analysis of the properties not only of classic random graphs but also in the interpretation of characteristic features of real-world networks. Computing the frequency of small subgraphs is a fundamental problem in network analysis, used across diverse domains: bioinformatics, social sciences, and infrastructure networks studies.