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THE FRIENDSHIP PARADOX FOR WEIGHTED AND DIRECTED NETWORKS

Part of: Mathematical sociology Markov processes Graph theory

Published online by Cambridge University Press:  18 September 2018

Kenneth S. Berenhaut  and
Hongyi Jiang
Kenneth S. Berenhaut
Affiliation:
Department of Mathematics and Statistics, Wake Forest University, 1834 Wake Forest Road, Winston Salem, NC, USA E-mails: berenhks@wfu.edu; jianh15@wfu.edu
Hongyi Jiang
Affiliation:
Department of Mathematics and Statistics, Wake Forest University, 1834 Wake Forest Road, Winston Salem, NC, USA E-mails: berenhks@wfu.edu; jianh15@wfu.edu
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Abstract

This paper studies the friendship paradox for weighted and directed networks, from a probabilistic perspective. We consolidate and extend recent results of Cao and Ross and Kramer, Cutler and Radcliffe, to weighted networks. Friendship paradox results for directed networks are given; connections to detailed balance are considered.

Keywords

configuration modeldetailed balancedirected networksfriendship paradoxrandom walksweighted networks

MSC classification

Primary: 05C81: Random walks on graphs
Secondary: 05C07: Vertex degrees 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 05C20: Directed graphs (digraphs), tournaments 91D30: Social networks 05C80: Random graphs
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 33 , Issue 1 , January 2019 , pp. 136 - 145
Copyright
Copyright © Cambridge University Press 2018 

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