Spectrum and coherence analysis in networks with noise disturbance

Abstract The Laplacian spectrum reflects the intrinsic characteristics and properties of a network, which can be used to quantify and evaluate performance metrics, such as connectivity, robustness, information propagation efficiency, consistency, and so on. Firstly, we systematically analyze the topological characteristics of a class of polygonal networks. Secondly, the Laplacian spectrum is calculated through matrix decomposition and an analysis of the characteristic polynomial. Finally, as an application of the obtained results, we derive expressions for the Kirchhoff index, the number of spanning trees, the mean first-passage time, and the network coherence.