CONSENSUS DYNAMICS WITH LEADER SELECTION IN HEXAGONAL NETWORKS

This study investigates the noise consensus dynamics in a class of networks with an initial hexagonal structure, where the vertices are subjected to white noise. Leveraging the network's self-similarity, a comprehensive spectral analysis is conducted. The research further explores the first- and second-order coherence in networks without leader nodes, as well as the first- and second-order coherence in networks with a single leader node and the first-order coherence in networks with dual leader nodes. Based on the specific topological properties of the network, explicit formulas for coherence under each consensus algorithm are derived. Taking UAV swarms as a representative example, the implications of the findings for leader node selection in multi-agent systems are analyzed, providing valuable theoretical insights into optimizing network performance.