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Subgraphs in preferential attachment models

Part of: Limit theorems Graph theory

Published online by Cambridge University Press:  03 September 2019

Alessandro Garavaglia  and
Clara Stegehuis
Alessandro Garavaglia*
Affiliation:
Eindhoven University of Technology
Clara Stegehuis*
Affiliation:
Eindhoven University of Technology
*
*Postal address: Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands.
*Postal address: Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands.
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Abstract

We consider subgraph counts in general preferential attachment models with power-law degree exponent $\tau > 2$. For all subgraphs H, we find the scaling of the expected number of subgraphs as a power of the number of vertices. We prove our results on the expected number of subgraphs by defining an optimization problem that finds the optimal subgraph structure in terms of the indices of the vertices that together span it and by using the representation of the preferential attachment model as a Pólya urn model.

Keywords

Preferential attachmentsubgraphtriangleclustering

MSC classification

Primary: 05C80: Random graphs
Secondary: 60F05: Central limit and other weak theorems
Type
Original Article
Information
Advances in Applied Probability , Volume 51 , Issue 3 , September 2019 , pp. 898 - 926
Copyright
© Applied Probability Trust 2019 

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