In many real-world networks, relationships often go beyond simple dyadic presence or absence; they can be positive, like friendship, alliance, and mutualism, or negative, characterized by enmity, disputes, and competition. To understand the formation mechanism of such signed networks, the social balance theory sheds light on the dynamics of positive and negative connections. In particular, it characterizes the proverbs, "a friend of my friend is my friend" and "an enemy of my enemy is my friend". In this work, we propose a nonparametric inference approach for assessing empirical evidence for the balance theory in real-world signed networks. We first characterize the generating process of signed networks with node exchangeability and propose a nonparametric sparse signed graphon model. Under this model, we construct confidence intervals for the population parameters associated with balance theory and establish their theoretical validity. Our inference procedure is as computationally efficient as a simple normal approximation but offers higher-order accuracy. By applying our method, we find strong real-world evidence for balance theory in signed networks across various domains, extending its applicability beyond social psychology.

翻译：在许多现实世界的网络中，关系往往超越简单的二元存在与否；它们既可以是积极的（如友谊、联盟与共生），也可以是消极的（以敌意、争端与竞争为特征）。为理解此类符号网络的形成机制，社会平衡理论揭示了正负连接的动态规律，特别体现在"朋友的朋友是朋友"和"敌人的敌人是朋友"这两类谚语中。本研究提出一种非参数推断方法，用于评估真实符号网络中平衡理论的经验证据。我们首先通过节点可交换性刻画符号网络的生成过程，提出一种非参数稀疏符号图模型。在该模型下，构建平衡理论群体参数的置信区间并建立其理论有效性。所提推断过程在计算效率上等同于简单正态近似，却能达到更高阶精度。通过该方法，我们在跨域真实符号网络中发现了支持平衡理论的强证据，将其适用性从社会心理学拓展至更广阔领域。