A PROBABILISTIC FRIENDSHIP NETWORK MODEL
2020 ◽
pp. 1-16
Keyword(s):
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.
2017 ◽
Vol 2017
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pp. 1-11
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2002 ◽
Vol 34
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pp. 609-625
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Vol 52
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pp. 1614-1640
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pp. 662-679
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pp. 2353-2368
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1995 ◽
Vol 32
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pp. 768-776
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