Structural Robustness of Consensus Models with Layered Correlated Graphs

This study analyzes network coherence in two-layer and three-layer networks with positive and negative inter-layer correlation patterns. Using algebraic graph theory, we construct the Laplacian matrices for different correlated graph structures and compute their Laplacian spectra. The impact of correlation patterns on network coherence is investigated for two-layer and three-layer structures, and numerical evaluations are performed. The results show that negative-correlation patterns yield better network coherence than positive ones. This work provides fundamental insights into the structural robustness of layered networks and offers theoretical guidance for the design of robust networked systems.