The equiconcept is a new topic in formal concept analysis and concept-cognitive learning, which provides a new idea for social network analysis. However, the existing equiconcept calculation methods first search out all formal concepts and then filter them, which reduces the calculation efficiency. And with the development of incremental computing, it is an important research topic to realize the calculation of the incremental equiconcept. To solve the above problems, this paper proposes an equiconcept calculation method based on incremental graph attribute topology. In view of the quantitative consistency between the attribute and object of the equiconcept, the proposed method defines the graph attribute topology on the graph formal context by optimizing the structure of the attribute topology. Furthermore, the one-to-one correspondence between the maximal complete polygon and the equiconcept in the graph property topology is proved. Combining this property with the formal concept search algorithm of the attribute topology, a method for directly calculating equiconcepts on the static graph formal context is proposed. On this basis, the influence of the new attribute and object on the maximal complete polygon in the graph attribute topology is further studied, and the direct calculation of incremental equiconcepts is completed. Experiments show that the direct calculation method can effectively improve the calculation speed of the equiconcept, and verify the feasibility and effectiveness of the proposed incremental equiconcept updating calculation.