This paper proposes an automated essay scoring (AES) model that utilizes the logical structure of an essay. We utilize the entire sentence containing the logical elements to estimate the relationships between the sentences. Then, the proposed method extracts relevant features using graph attention networks that can consider the graph structure and combines with the conventional AES model. Experiments conducted on the ASAP dataset demonstrated that the proposed model obtains higher accuracy than the baseline and conventional methods. Furthermore, it achieved higher accuracy even in cases of random or absent argumentative structures, as well as those estimated by LLMs.