Effect of Topological Structure and Coupling Strength in Weighted Multiplex Networks

Abstract

Algebraic connectivity (second smallest eigenvalue of the supra-Laplacian matrix of the underlying multilayer network) and inter-layer coupling strength play an important role in the diffusion processes on the multiplex networks. In this work, we study the effect of inter-layer coupling strength, topological structure on algebraic connectivity in weighted multiplex networks. The results show a remarkable transition in the value of algebraic connectivity from classical cases where the inter-layer coupling strength is homogeneous. We investigate various topological structures in multiplex networks using configuration model, the Barabasi-Albert model (BA) and empirical data-set of multiplex networks. The threshold value \(d_c^{'}\) is found smaller in heterogeneous networks for all the multiplex networks as compared to the homogeneous case. Experimental results reveal that the topological structure (average clustering coefficient) and inter-layer coupling strength has considerable effect on threshold values for the algebraic connectivity.