Nonparametric Inference for Balance in Signed Networks

TL;DR

This paper introduces a nonparametric inference method to evaluate the social balance theory in signed networks, providing a statistically valid and computationally efficient approach with real-world applications.

Contribution

It develops a nonparametric sparse signed graphon model and constructs confidence intervals for balance theory parameters, extending analysis to diverse real-world signed networks.

Findings

Strong evidence for balance theory in various real-world signed networks.

The inference method is computationally efficient and more accurate than normal approximation.

The approach generalizes the applicability of balance theory beyond social psychology.

Abstract

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.