Nonparametric inference for balance in signed networks

Abstract In many real-world networks, relationships often go beyond simple dyadic presence or absence; they can be positive, such as friendship, alliance and mutualism, or negative, characterized by enmity, disputes and competition. To understand the mechanisms of formation of such signed networks, 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 to assessing empirical evidence for 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 yields 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.