Abstract: This paper extends the rules for simplification of weighted graph as established by one of the authors. It suits non-directional Coates figures as well as directional Coates figures. Meanwhile it suits the calculation of eigenvectors but also suits to solve system of linear equations.In order to apply such rules to finite element calculation of linearly elastic bodies, the concepts of rigidity weighted graph, mass weighted graph and characteristic weighted graph are defined. The graph method is thus introduced into finite element analysis of linearly elastic body.