Every finite tree has at least as many positive as negative friendship-bias vertices, with an explicit gap bound, and infinite Galton-Watson trees have computable densities of all three vertex types.
Feld, Why your friends have more friends than you do, American Journal of Sociology 96 (1991), 1464–1477
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The friendship paradox for trees
Every finite tree has at least as many positive as negative friendship-bias vertices, with an explicit gap bound, and infinite Galton-Watson trees have computable densities of all three vertex types.