Network Coherence in a Family of Book Graphs

Abstract

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In this paper, we study network coherence characterizing the consensus behaviors with additive noise in a family of book graphs. It is shown that the network coherence is determined by the eigenvalues of the Laplacian matrix. Using the topological structures of book graphs, we obtain recursive relationships for the Laplacian matrix and Laplacian eigenvalues and further derive exact expressions of the network coherence. Finally, we illustrate the robustness of network coherence under the graph parameters and show that the parameters have distinct effects on the coherence.

Keywords

• consensus
• coherence
• book graph
• Laplacian spectra
• recursive