An Eigen-decomposition Free Method for Computing Graph Fourier Transform Centrality

Abstract

In this paper, an eigen-decomposition free method is presented to compute the graph Fourier transform centrality (GFTC) of complex network. For conventional computation method of GFTC, it needs to compute eigen-decomposition of graph Laplacian matrix for obtaining the transform basis of graph Fourier transform (GFT), which may not be computable for larger networks. To tackle this problem, the graph filtering method is applied to transform the spectral-domain GFTC computation task to vertex-domain one such that GFTC can be computed by using graph filter which is easily designed by the least squares (LS) method. Finally, the centrality computations of the Taipei metro network and karate-club social network are used to show the effectiveness of the proposed GFTC computation method.