A PROBABILISTIC FRIENDSHIP NETWORK MODEL. Issue 1 (January 2022)

• Record Type: Journal Article
• Authors: Dizon-Ross, Rebecca; Ross, Sheldon M.
• Is Part Of: Probability in the engineering and informational sciences. Volume 36:Issue 1(2022)
• Page Start: 1
• Page End: 16
• Publication Date: 2022-01
• Subjects: associated random variables -- friendless individuals -- friendship model -- friendship paradox -- stochastic network -- Poisson approximation; Probabilities -- Periodicals; Engineering -- Statistical methods -- Periodicals; Information science -- Statistical methods -- Periodicals; 519.202462
• DOI: 10.1017/S0269964820000339
• Languages: English
• ISSNs: 0269-9648

Abstract

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.