Abstract

Friendship and antipathy exist in concert with one another in real social networks. Despite the role they play in social interactions, antagonistic ties are poorly understood and infrequently measured. One important theory of negative ties that has received relatively little empirical evaluation is balance theory, the codification of the adage “the enemy of my enemy is my friend” and similar sayings. Unbalanced triangles are those with an odd number of negative ties, and the theory posits that such triangles are rare. To test for balance, previous works have used a permutation test on the edge signs. The flaw in this method, however, is that it assumes that negative and positive edges are interchangeable. In reality, they could not be more different. Here, we propose a novel test of balance that accounts for this discrepancy and show that our test is more accurate at detecting balance. Along the way, we prove asymptotic normality of the test statistic under our null model, which is of independent interest. Our case study is a novel dataset of signed networks we collected from 32 isolated, rural villages in Honduras. Contrary to previous results, we find that there is only marginal evidence for balance in social tie formation in this setting.

摘要

在真实的社交网络中，友谊和反感是同时存在的。尽管它们在社会互动中发挥着作用，但对立关系却知之甚少，也很少衡量。一种相对较少受到实证评价的重要负面关系理论是平衡理论，它是格言“敌人的敌人是我的朋友”和类似说法的编纂。不平衡三角形是具有奇数个负连接的三角形，该理论认为这种三角形很少见。为了测试平衡，以前的作品在边缘标志上使用了置换测试。然而，这种方法的缺陷是它假设负边沿和正边沿是可以互换的。实际上，它们的差异再大不过了。这里，我们提出了一种新的平衡测试来解释这种差异，并表明我们的测试在检测平衡方面更准确。在此过程中，我们证明了在我们的空模型下测试统计量的渐近正态性，这是独立感兴趣的。我们的案例研究是我们从洪都拉斯的 32 个偏远乡村收集的签名网络的新数据集。与之前的结果相反，我们发现在这种情况下，社会联系形成的平衡只有微不足道的证据。