A person’s enemies have more enemies, on average, than a person does.
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 24,678 people living in 176 villages in rural Honduras. We \amir{empirically} show that, for a \amir{(pure)} 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 non-topological 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.
Histograms of $\delta_g$ and $\delta_l$ for undirected (symmetrized) networks among 176 village networks. The histograms of (pure) enmity and friendship paradoxes are provided in panels A and D, respectively. Other panels represent the histograms of enmity paradox strengths for the mixed worlds. The histogram in panel B shows the global and local paradox distributions for the difference between the number of our enemies and the number of enemies of our friends, while panel C represents the difference between the number of our friends and the number of friends of our enemies.
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.
@article{ghasemian2023enmity,title={The Enmity Paradox},author={Ghasemian, Amir and Christakis, Nicholas A},journal={Scientific Reports},volume={13},issue={1},pages={20040},year={2023},}
