In addition to various studies in the field of Korean traditional music on the transition process and characteristics of Mitdodeuri, there was a study on Haegeum melody analysis applying Topological Data Analysis. It is part of the recently emerging artificial intelligence music research. It is necessary to review whether the analysis adequately reflects the characteristics of the music. In particular, the analysis method of TDA was made by substituting each node, which is the unit of the combination of pitch and length. Therefore, it is necessary to verify whether this matches the characteristics of music that are generally recognized. Accordingly, melodies repeated the same as before were found in Mitdodeuri Haegeum melody. Again, the whole melody was divided into melodic fragments of one Jangdan or less. Afterward, it was classified into original melody and repeated/transformed melody. As a result of comparing the pattern of melodies and previous studies, the formation of the cycle in TDA was related to melodic lines. And it was found that the ‘repeat-and-return’ pattern of Mitdodeuri revealed by the cycle structure from TDA was quite consistent with the melodic structure of Mitdodeuri.