  The Friendship Paradox--the principle that "your friends have more friends
than you do"--is a combinatorial fact about degrees in a graph; but given that
many web-based social activities are correlated with a user's degree, this fact
has been taken more broadly to suggest the empirical principle that "your
friends are also more active than you are." This Generalized Friendship
Paradox, the notion that any attribute positively correlated with degree obeys
the Friendship Paradox, has been established mathematically in a network-level
version that essentially aggregates uniformly over all the edges of a network.
Here we show, however, that the natural node-based version of the Generalized
Friendship Paradox--which aggregates over nodes, not edges--may fail, even for
degree-attribute correlations approaching 1. Whether this version holds depends
not only on degree-attribute correlations, but also on the underlying network
structure and thus can't be said to be a universal phenomenon. We establish
both positive and negative results for this node-based version of the
Generalized Friendship Paradox and consider its implications for social-network
data.
