Population-level Balance in Signed Networks

TL;DR

This paper introduces a latent space statistical model for signed networks that incorporates balance theory, enabling better understanding and visualization of complex positive and negative relationships in real-world networks.

Contribution

It proposes a novel population-level balance concept and a scalable latent space model for signed networks, with theoretical error bounds and practical applications.

Findings

The model effectively captures balance theory in signed networks.

Simulation studies confirm the accuracy of the estimates.

Application to WWII data yields interpretable insights.

Abstract

Statistical network models are useful for understanding the underlying formation mechanism and characteristics of complex networks. However, statistical models for \textit{signed networks} have been largely unexplored. In signed networks, there exist both positive (e.g., like, trust) and negative (e.g., dislike, distrust) edges, which are commonly seen in real-world scenarios. The positive and negative edges in signed networks lead to unique structural patterns, which pose challenges for statistical modeling. In this paper, we introduce a statistically principled latent space approach for modeling signed networks and accommodating the well-known \textit{balance theory}, i.e., ``the enemy of my enemy is my friend'' and ``the friend of my friend is my friend''. The proposed approach treats both edges and their signs as random variables, and characterizes the balance theory with a novel and natural notion of population-level balance. This approach guides us towards building a class of balanced inner-product models, and towards developing scalable algorithms via projected gradient descent to estimate the latent variables. We also establish non-asymptotic error rates for the estimates, which are further verified through simulation studies. In addition, we apply the proposed approach to an international relation network, which provides an informative and interpretable model-based visualization of countries during World War II.