A Rational Graph Filter Method for GFT Centrality Computation

Graph Fourier transform (GFT) is an important tool for analyzing the irregular graph signals collected from various real-world networks. One of its applications is the graph Fourier transform centrality (GFTC) which has been developed to find the influential nodes in the graphical representations of networks. In the traditional GFTC computation method, the eigen-decomposition of Laplacian matrix needs to be calculated for obtaining the GFT basis to compute GFTC. To reduce the computational complexity, a rational graph filter (RGF) method is presented in this paper. The main technique is that the spectral-domain computational task is converted to the vertex-domain one by using Parseval’s theorem of GFT. The Pade method and Maclaurin series expansion are applied to obtain the filter coefficients of RGF when the weight function of GFTC is specified. Finally, the Taipei metro network is used to demonstrate the effectiveness of GFTC index for identifying the important stations in the metro network.