Optimizing Superdiffusion of Multiplex Networks Based on Spectral Graph Theory

Superdiffusion refers to the faster diffusion process in a multiplex network compared to that in an individual network. In this work, we study how interlayer connectivity affects the diffusion performance of a multiplex network. Based on spectral graph theory, we explore the principles of superdiffusion in multiplex networks. We prove that in a duplex network with identical structures, superdiffusion cannot occur under one-to-one interlayer connections. In addition, we prove that the dissimilarity of the Fiedler vector significantly enhances the network superdiffusion performance, which can lead to superdiffusion when selecting nodes with differential eigenvector components in the Fiedler vector for interlayer connections. We also prove that the upper bound of network diffusion with interlayer crossing-connections is limited by the maximum difference of the eigenvector components in the Fiedler vector. Finally, we verify the effectiveness of the theoretical results by numerical analysis.