Disagreement and Antagonism in Signed Networks: A Survey

Signed networks refer to a class of network systems including not only cooperative but also antagonistic interactions among nodes. Due to the existence of antagonistic interactions in signed networks, the agreement of nodes may not be established, instead of which disagreement behaviors generally emerge. This paper reviews several different disagreement behaviors in signed networks under the single-integrator linear dynamics, where two classes of topologies, namely, the static topology and the dynamic topology, are considered. For the static signed networks with the adjacency weights as (time-varying) scalars, we investigate the convergence behaviors and the fluctuation behaviors with respect to fixed topologies and switching topologies, respectively, and give some brief introductions on the disagreement behaviors of general time-varying signed networks. Correspondingly, several classes of behavior analysis approaches are also provided. For the dynamic signed networks with the adjacency weights as transfer functions or linear time-invariant systems, we show the specific descriptions and characteristics of them such that the disagreement behaviors can be obtained by resorting to the derived static signed graphs. Furthermore, we give their applications to the behavior analysis of static signed networks in the presence of high-order dynamics or communication delays.