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13 - Intersection Graphs

from Part III - Modeling Complex Networks

Published online by Cambridge University Press:  02 March 2023

Alan Frieze
Affiliation:
Carnegie Mellon University, Pennsylvania
Michał Karoński
Affiliation:
Adam Mickiewicz University, Poznań, Poland
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Summary

A graph is an intersection graph if we assign to each vertex a set from some family S so that there is an edge between two of its vertices when respective sets intersect. Depending on the choice of family S, often reflecting some geometric configuration, one can consider, for example, interval graphs defined as the intersection graphs of intervals on the real line, unit disk graphs defined as the intersection graphs of unit disks on the plane, etc. In this chapter, we will discuss properties of random intersection graphs, where the family S is generated in a random manner. In this chapter, we discuss the properties of binomial intersection random graphs and random geometric graphs.

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Publisher: Cambridge University Press
Print publication year: 2023

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  • Intersection Graphs
  • Alan Frieze, Carnegie Mellon University, Pennsylvania, Michał Karoński, Adam Mickiewicz University, Poznań, Poland
  • Book: Random Graphs and Networks: A First Course
  • Online publication: 02 March 2023
  • Chapter DOI: https://doi.org/10.1017/9781009260268.017
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  • Intersection Graphs
  • Alan Frieze, Carnegie Mellon University, Pennsylvania, Michał Karoński, Adam Mickiewicz University, Poznań, Poland
  • Book: Random Graphs and Networks: A First Course
  • Online publication: 02 March 2023
  • Chapter DOI: https://doi.org/10.1017/9781009260268.017
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Intersection Graphs
  • Alan Frieze, Carnegie Mellon University, Pennsylvania, Michał Karoński, Adam Mickiewicz University, Poznań, Poland
  • Book: Random Graphs and Networks: A First Course
  • Online publication: 02 March 2023
  • Chapter DOI: https://doi.org/10.1017/9781009260268.017
Available formats
×