Yale Institute for Network Science, Yale University, New Haven, CT, 06511, USA.
Sci Rep. 2023 Nov 16;13(1):20040. doi: 10.1038/s41598-023-47167-9.
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 empirically 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, which we refer to as the "mixed-world 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.
社交网络中的“友谊悖论”指出，平均而言，“你的朋友比你拥有更多的朋友”。在这里，我们从理论和实证两个方面探讨了一个相关但被忽视的悖论，我们称之为“敌意悖论”。我们使用了来自生活在洪都拉斯 176 个村庄的 24678 人的实证数据。我们从实证上证明，对于一个真实的负向无向网络（通过对称化对抗性交互创建），这个悖论与正向世界中的悖论一样存在。具体来说，一个人的敌人平均来说比这个人拥有更多的敌人。此外，在一个包含正向和负向联系的混合世界中，我们从理论和实证两个方面研究了悖论存在的条件，我们称之为“混合世界悖论”，发现例如，一个人的朋友通常比这个人拥有更多的敌人。我们还在真实数据中确认了非拓扑属性的“广义敌意悖论”，类似于广义友谊悖论（例如，一个人的敌人平均来说比这个人更富有）。因此，社交网络中友谊和敌意的度数分布的自然变化可能会扭曲人们对社交世界的看法。
