  The "friendship paradox" of social networks states that, on average, "your
friends have more friends than you do." Here, we theoretically and empirically
explore a related and overlooked paradox we refer to as the "enmity paradox."
We use empirical data from 24,687 people living in 176 villages in rural
Honduras. We show that, for a real negative undirected network (created by
symmetrizing antagonistic interactions), the paradox exists as it does in the
positive world. Specifically, a person's enemies have more enemies, on average,
than a person does. Furthermore, in a mixed world of positive and negative
ties, we study the conditions for the existence of the paradox, both
theoretically and empirically, finding that, for instance, a person's friends
typically have more enemies than a person does. We also confirm the
"generalized" enmity paradox for nontopological attributes in real data,
analogous to the generalized friendship paradox (e.g., the claim that a
person's enemies are richer, on average, than a person is). As a consequence,
the naturally occurring variance in the degree distribution of both friendship
and antagonism in social networks can skew people's perceptions of the social
world.
