Rigid foldability is an important feature of the paper folding mechanism, allowing continuous movement along a predetermined crease between the folded and unfolded state without stretching or bending the surface. It has great potential in engineering applications. In view of the difficulty in the analysis of the freedom degree of multi-vertex origami mechanism, a method using adjacency matrix to analyze the freedom degree of rigid origami is proposed. The adjacency matrix is used to represent the connection relationship between vertices, then, by introducing an elimination matrix, the process of determining the motion state is described by matrix multiplication. The number of constraints is determined by calculating the sum of the row elements corresponding to the vertices, which avoid the calculation error of the freedom degree of the vertices of the cross crease. Based on the analysis of the freedom degree of the single-vertex 4-fold origami pattern, the topology is used to analyze the freedom degree of multi-vertex triangular rigid origami pattern. Finally, the correctness of the calculation results of the freedom degree of the rigid origami pattern is checked by software simulation.