Proposal of the Network Resonance Method for Estimating Eigenvalues of the Scaled Laplacian Matrix

Satoshi Furutani, Chisa Takano, Masaki Aida

Abstract: Eigenvalues of the Laplacian matrix play an important role in characterizing structural and dynamical properties of networks. In the procedure for calculating eigenvalues of the Laplacian matrix, we need to get the Laplacian matrix that represents structures of the network. Since the actual structure of networks and the strength of links are difficult to know, it is difficult to determine elements of the Laplacian matrix. To solve this problem, our previous study proposed a concept of the network resonance method, which is for estimating eigenvalues of the scaled Laplacian matrix using resonance of oscillation dynamics on networks. This method does not need a priori information about the network structure. In this research, we investigate feasibility of the network resonance method, and show that the method can estimate eigenvalues of the scaled Laplacian matrix of the entire network through observations of oscillation dynamics even if observable nodes are restricted to a part of network.