  The friendship paradox refers to the sociological observation that, while the
people's assessment of their own popularity is typically self-aggrandizing, in
reality they are less popular than their friends. The generalized friendship
paradox is the average alter superiority observed empirically in social
settings, scientific collaboration networks, as well as online social media. We
posit a quality-based network growth model in which the chance for a node to
receive new links depends both on its degree and a quality parameter. Nodes are
assigned qualities the first time they join the network, and these do not
change over time. We analyse the model theoretically, finding expressions for
the joint degree-quality distribution and nearest-neighbor distribution. We
then demonstrate that this model exhibits both the friendship paradox and the
generalized friendship paradox at the network level, regardless of the
distribution of qualities. We also show that, in the proposed model, the degree
and quality of each node are positively correlated regardless of how node
qualities are distributed.
