Finding Most Influential Inter-Layer Edges to Enhance Diffusion on Two-Layer Interconnected Networks
Xingjun Wang, Yujuan Han · 2023
This note is to give the theoretical analysis for the selection of interconnections to maximize the diffusion speed on interconnected networks where two layers are directed. The second smallest eigenvalue (in terms of real part) of the supra-Laplacian matrix is considered as a metric. Based on the matrix perturbation theory, we derive a first-order approximation of the second smallest eigenvalue, resulting in a scoring of inter-layer edges. We propose an algorithm for selecting connector nodes and verify its effectiveness through simulation examples.