Adaptive Control Scheme for Clustering of Nodes Based on the Signs of Connections in Dynamical Signed Networks

The concept of clustering has garnered significant attention within the field of complex networks. Numerous clustering algorithms have been documented in the extant academic literature. However, most of them consider static signed networks, which are not suitable for dynamical networks. For dynamical signed networks, there is a class of algorithms called cluster dynamics. Nevertheless, they regard the connection to be time-invariant, which is a constraint. In this paper, for a kind of dynamical signed networks with time-varying connections, we discuss the adaptive control scheme for clustering of nodes, such that the network evolves asymptotically into a classifiable network that contains several friends’ groups with clear sign boundaries. In other words, through the careful design of the controller for the nodes and the establishment of coupling relationships between the nodes and their connections, we ensure that the connection of the dynamical signed network can approximate asymptotically the connection of a given classifiable network, as measured by the concept of uniformly ultimately bounded (UUB). Finally, the simulation is used to illustrate the validity of the method proposed in this paper.