The mechanism of three?order Rubik??s Cube ( RC) has the characteristics of recombination and variable degree of freedom, and it is difficult to accurately describe the degree of its freedom. This paper takes RC as the research object, and the adjacency matrix is constructed based on topology and graph theory in order to describe the variation rule of topological configuration in the single layer rotation of RC. In this paper, the degree of freedom of the RC in any shape can be described by defining the concept of entanglement degree of freedom, establishing a set of adjacency matrix, and determining the degree of freedom of the RC which is attributed to the number of non?zero elements in the set of adjacent matrix. The prime number is proposed to describe the rotation of the RC combined with the rotation recognition of RC, which is simple and convenient for computer processing. The research contents in this paper are beneficial to the study of RC from the perspective of mechanism science. Meanwhile, it is of great significance to the study of other complex mechanisms with variable degrees of freedom.