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4 - Connected Components in Configuration Models

from Part II - Connected Components in 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 the local limit of the configuration model, we identify when it has a giant component and find its size and degree structure. We give two proofs, one based on a “the giant is almost local” argument, and another based on a continuous-time exploration of the connected components in the configuration model. Further results include its connectivity transition.

Keywords

configuration modelsuniform random graphs with prescribed degreeslocal convergenceconnected componentsconnectivitybranching processesunimodular branching processesbranching processes with infinite meangiant componentgiant is almost local
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Chapter
Information
Random Graphs and Complex Networks , pp. 138 - 188
Publisher: Cambridge University Press
Print publication year: 2024

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