Research: Mathematical properties of signed networks

Overview

My research focuses on the mathematical analysis of signed networks — systems where interactions can be either positive or negative, such as alliances and conflicts in international relations, excitatory and inhibitory links in neural networks, or cooperative and competitive dynamics in ecology and economics. While network science has traditionally overlooked negative edges, I find them essential to understanding systems shaped by antagonism, inhibition, or polarization.

The core aim of my research is to develop robust mathematical tools to analyze the structure and dynamics of signed networks. This includes:

• Defining and characterizing emergent features like local and global balance, effective enmities, and polarization.

• Building theoretically-sounded algorithms to detect opposing factions, find central nodes, and reconstruct signed networks from noisy data.

• Understand how the structure of signed networks affects dynamical processes taking place on them.

• Applying the theoretical results to practical settings in geopolitics, social systems, finance, and biology.