Network coherence of weighted duplex networks: Exact results

Abstract

The Laplacian spectra are often used to characterize topological properties and dynamical characteristics of the networks. In this paper, we analytically calculate the network coherence quantified by the Laplacian spectra, which is a measurement of the extent of consensus in the coupled systems with the noise. Due to complex interactions between two coupled networks, we choose three types of weighted duplex networks with an aim of obtaining their exact solutions of the network coherence. Based on the network structures and matrix theories, we provide analytical expressions of the coherence regarding the network size and weights and further study the robustness of the coherence under network parameters. We finally show that smaller network sizes and larger weights will lead to better coherence and the best coherence happens in a duplex network because there are more connections between the layers.