Method for Estimating the Eigenvectors of a Scaled Laplacian Matrix Using the Resonance of Oscillation Dynamics on Networks

Satoshi Furutani, Chisa Takano, Masaki Aida

Abstract: Spectral graph theory gives a useful approach to analyzing network structure based on the adjacency matrix or the Laplacian matrix that represents the network topology and link weights. However, in large scale and complex social networks, since it is difficult to know the network topology and link weights, we cannot determine the components of these matrices directly. To solve this problem, we consider a method for indirectly determining a Laplacian matrix from its eigenvalues and eigenvectors. As the first step, our prior study proposed a method for estimating eigenvalues of a Laplacian matrix by using the resonance of oscillation dynamics on networks with no a priori information about the network structure, and showed the effectiveness of this method. In this paper, we propose a method for estimating the eigenvectors of a Laplacian matrix by once again using the resonance of oscillation dynamics on networks.