In the recouping theorem and the graph calculation for loop quantum gravity, it is proved that the action of metric matrix operator on Gaussian weave state is an eigenaction, and the representation matrix elements of the metric operator and their expectation values are calculated. The values of the length of tangent vectors with 4 edges (P=1) adjacent to the vertex of Gaussian weave state ψp, as well as the angles between them, are also obtained in the cases of k=0 and k=2.