Property analysis and coherence dynamics for tree-symmetric networks with noise disturbance

In this paper, we investigate the leaderless and the leader–follower coherence of tree-symmetric networks. Firstly, the analytical expressions for the product and the sum of the reciprocals of all nonzero Laplacian eigenvalues of tree-symmetric networks are computed. Secondly, comparing the leaderless and leader–follower coherence, the existence of leader nodes and network parameters have a great impact on the coherence in the noisy environment. Finally, the Laplacian eigenvalues of tree-symmetric networks were utilized to analyze other properties of the network. These research results have certain theoretical significance for the promotion of distributed system and block chain technology.