The graph signal modeling is carried out based on fault recording starting message, and based on the improved eigenvector centrality algorithm, the diagnosis method for power grid fault is proposed. Firstly, the fault wave network diagram is constructed according to the fault recording starting message of relay protection and fault recording master station. Secondly, the analysis method of graph smoothness is used to judge whether the fault occurs and to identify the fault type. Finally, based on the improved eigenvector centrality algorithm, the fault component is identified and visually displayed. The validity of the proposed algorithm is verified by simulation, which is helpful for the regulators to quickly analyze and judge the situation of grid fault and to collect the important fault recording data for analysis and checking so as to improve the efficiency of recording analysis.