Algebraic-Graphical Approach for Signed Dynamical Networks
Baras, John, S.
Date: December 12 - December 15, 2017
A signed network is a network with each link associated with a positive or negative sign. Models for nodes interacting over such signed networks, where two types of interactions are deﬁned along the positive and negative links, respectively, arise from various biological, social, political, and economical systems. Starting from standard consensus dynamics, there are two basic types of negative interactions along negative links, namely state ﬂipping or relative-state ﬂipping. In this paper, we provide an algebraic-graphical method serving as a systematic tool of studying these dynamics over signed networks. Utilizing generalized Perron-Frobenius theory, graph theory, and elementary algebraic recursions, we show this method is useful to establish a series of basic convergence results for dynamics over signed networks.Download Full Paper