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A PROBABILISTIC FRIENDSHIP NETWORK MODEL

Published online by Cambridge University Press:  03 June 2020

Rebecca Dizon-Ross  and
Sheldon M. Ross Open the ORCID record for Sheldon M. Ross [Opens in a new window]
Rebecca Dizon-Ross
Affiliation:
Booth School of Business, University of Chicago, Chicago, Illinois60637, USA E-mail: rdr@chicagobooth.edu
Sheldon M. Ross
Affiliation:
Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, California90089, USA E-mail: smross@usc.edu
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Abstract

We consider a friendship model in which each member of a community has a latent value such that the probability that any two individuals are friends is a function of their latent values. We consider such questions as does information that i and j are both friends with k make it more likely that i and j are themselves friends. Among other things, we show that for fixed sets S and T, the more friends that i has in S, then the stochastically more friends i has in T. We consider how a variation of the friendship paradox applies to our model. We also study the distribution of the number of friendless individuals in the community and derive a bound on the total variation distance between it and a Poisson with the same mean.

Keywords

associated random variablesfriendless individualsfriendship modelfriendship paradoxstochastic networkPoisson approximation
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 36 , Issue 1 , January 2022 , pp. 1 - 16
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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