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8 - Small-World Phenomena in Preferential Attachment Models

from Part III - Small-World Properties of Random Graphs

Published online by Cambridge University Press:  08 February 2024

Remco van der Hofstad
Remco van der Hofstad
Affiliation:
Technische Universiteit Eindhoven, The Netherlands
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Summary

In this chapter we investigate graph distances in preferential attachment models. We focus on typical distances as well as the diameter of preferential attachment models. We again rely on path-counting techniques, as well as local limit results. Since the local limit is a rather involved quantity, some parts of our analysis are considerably harder than those in Chapters 6 and 7.

Keywords

preferential attachment modelsPólya urn representation of preferential attachment modelstypical distancesdiametersmall-world networksultra-small networkspath-counting techniquespower-iteration methoddistances in the core
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Chapter
Information
Random Graphs and Complex Networks , pp. 326 - 380
Publisher: Cambridge University Press
Print publication year: 2024

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