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7 - Small-World Phenomena in Configuration Models

from Part III - Small-World Properties of Random Graphs

Published online by Cambridge University Press:  08 February 2024

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

In this chapter we investigate the distance structure of the configuration model by investigating its typical distances and its diameter. We adapt the path-counting techniques in Chapter 6 to the configuration model, and obtain typical distances from the “giant is almost local” proof. To understand the ultra-small distances for infinite-variance degree configuration models, we investigate the generation growth of infinite-mean branching processes. The relation to branching processes informally leads to the power-iteration technique that allows one to deduce typical distance results in random graphs in a relatively straightforward way.

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Publisher: Cambridge University Press
Print publication year: 2024

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