Early Typical Vertices in Subcritical Random Graphs of Preferential Attachment Type

Mörters, Peter; Schleicher, Nick

doi:10.4230/LIPIcs.AofA.2024.14

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Document Identifiers

DOI: 10.4230/LIPIcs.AofA.2024.14
URN: urn:nbn:de:0030-drops-204493

Author Details

Peter Mörters

University of Cologne, Germany

Nick Schleicher

University of Cologne, Germany

Acknowledgements

This paper contains results from the second author’s Master thesis.

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Peter Mörters and Nick Schleicher. Early Typical Vertices in Subcritical Random Graphs of Preferential Attachment Type. In 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 302, pp. 14:1-14:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.AofA.2024.14

Abstract

We study the size of the connected component of early typical vertices in a subcritical inhomogeneous random graph with a kernel of preferential attachment type. The principal tools in our analysis are, first, a coupling of the neighbourhood of a typical vertex in the graph to a killed branching random walk and, second, an asymptotic result for the number of particles absorbed at the killing barrier in this branching random walk.

Subject Classification

ACM Subject Classification

Mathematics of computing → Random graphs
Mathematics of computing → Paths and connectivity problems
Mathematics of computing → Markov processes

Keywords

Inhomogeneous random graphs
preferential attachment
networks
subcritical behaviour
size of components
connectivity
coupling
branching random walk
random tree

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