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The degree-wise effect of a second step for a random walk on a graph

Part of: Markov processes Graph theory Combinatorial probability Mathematical sociology

Published online by Cambridge University Press:  16 January 2019

Kenneth S. Berenhaut ,
Hongyi Jiang ,
Katelyn M. McNab  and
Elizabeth J. Krizay
Kenneth S. Berenhaut*
Affiliation:
Wake Forest University
Hongyi Jiang*
Affiliation:
Johns Hopkins University
Katelyn M. McNab*
Affiliation:
Wake Forest University
Elizabeth J. Krizay*
Affiliation:
Georgia Institute of Technology
*
* Postal address: Department of Mathematics and Statistics, Wake Forest University, Winston-Salem, NC 27109, USA.
*** Postal address: Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD 21218, USA.
* Postal address: Department of Mathematics and Statistics, Wake Forest University, Winston-Salem, NC 27109, USA.
**** Postal address: H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA.
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Abstract

In this paper we consider the degree-wise effect of a second step for a random walk on a graph. We prove that under the configuration model, for any fixed degree sequence the probability of exceeding a given degree threshold is smaller after two steps than after one. This builds on recent work of Kramer et al. (2016) regarding the friendship paradox under random walks.

Keywords

Friendship paradoxgraphrandom walkconfiguration model

MSC classification

Primary: 05C81: Random walks on graphs
Secondary: 05C07: Vertex degrees 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60C05: Combinatorial probability 91D30: Social networks 05C80: Random graphs
Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 4 , December 2018 , pp. 1203 - 1210
Copyright
Copyright © Applied Probability Trust 2018 

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