This paper discusses the approximate solution to the weighted graph matching problem (WGMP) both for undirected and directed graphs. WGMP is the problem of finding the optimum matching between two weighted graphs, which are graphs with weights at each arc. The proposed method employs an analytic approach using the eigen-decomposition of the adjacency matrix (in the case of undirected matching problem) or the singular value decomposition of the incidence matrix (in the case of directed graph matching problem) of a given graph. A technique for reducing the execution time to search for the solution is given. Simulation experiments are also given to evaluate the performance of the proposed method.