Structural robustness and optimization of leader-follower coherence in star-coupled networks

Abstract In this paper, we investigate the structural robustness and optimization of leader-follower coherence, quantified by the eigenvalues of the grounded Laplacian matrix, which measures the deviation between leaders and followers. To examine the impacts of network couplings and leader assignments on coherence, we select star-coupled networks as base models and introduce three types of coupling forms. By utilizing regular network structures, we derive analytical expressions for leader-follower coherence with respect to network parameters and evaluate the performance of coherence under various leader assignments. In addition, for achieving the lowest coherence in a network connected by a path graph, we propose an optimization algorithm that involves adding edges among the followers to enhance coherence.