A modelling and computational study of the frustration index in signed networks

TL;DR

This paper introduces three new binary linear programming models for efficiently computing the frustration index in large signed networks, significantly outperforming existing methods in speed and accuracy.

Contribution

The authors develop and validate three novel binary linear programming models that compute the frustration index exactly and efficiently for large-scale signed networks.

Findings

Models solve networks with over 15,000 edges in less than a minute.

Models outperform all existing approaches in speed and accuracy.

Extensive analysis confirms the models' superiority over heuristic methods.

Abstract

Computing the frustration index of a signed graph is a key step toward solving problems in many fields including social networks, political science, physics, chemistry, and biology. The frustration index determines the distance of a network from a state of total structural balance. Although the definition of the frustration index goes back to the 1950's, its exact algorithmic computation, which is closely related to classic NP-hard graph problems, has only become a focus in recent years. We develop three new binary linear programming models to compute the frustration index exactly and efficiently as the solution to a global optimisation problem. Solving the models with prioritised branching and valid inequalities in Gurobi, we can compute the frustration index of real signed networks with over 15000 edges in less than a minute on inexpensive hardware. We provide extensive performance analysis for both random and real signed networks and show that our models outperform all existing approaches by large factors. Based on solve time, algorithm output, and effective branching factor we highlight the superiority of our models to both exact and heuristic methods in the literature.