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11 - Small World

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

Large real-world networks although being globally sparse, in terms of the number of edges, have their nodes/vertices connected by relatively short paths. In addition, such networks are locally dense, i.e., vertices lying in a small neighborhood of a given vertex are connected by many edges. This observation is called the “small-world” phenomenon, and it has generated many attempts, both theoretical and experimental, to build and study appropriate models of small-world networks. The first attempt to explain this phenomenon and to build a more realistic model was introduced by Watts and Strogatz in 1998 followed by the publication of an alternative approach by Kleinberg in 2000. The current chapter is devoted to the presentation of both models.

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Publisher: Cambridge University Press
Print publication year: 2023

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  • Small World
  • 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/10.1017/9781009260268.015
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  • Small World
  • 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/10.1017/9781009260268.015
Available formats
×

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.

  • Small World
  • 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/10.1017/9781009260268.015
Available formats
×