PC Seminar: Incorporating Negative Connections: Signed Networks and Their Properties

Abstract: Two competing types of interactions often play an important part in shaping system behavior, such as activatory or inhibitory functions in biological systems. Hence, signed networks, where each connection can be either positive or negative, have become popular models over recent years. In this talk, I will first introduce a classification of signed networks into balanced, antibalanced or strictly balanced ones, and then characterise each type of signed networks in terms of the spectral properties of the signed weighted adjacency matrix. In particular, the spectral radius of the matrix with signs is smaller than that without if and only if the signed network is strictly unbalanced. These properties are important to understand the dynamics on signed networks, both linear and nonlinear ones. Later in this talk, I will show consistent patterns in a linear and a nonlinear dynamics, depending on their type of balance, together with the numerical experiments on both synthetic and real networks

This is a seminar in our seminar series on Probability and Combinatorics (PC).