Fuzzy information such as human relation and opinion survey is effectively represented as fuzzy graph. However, it is very difficult to clarify the global structure of the fuzzy graph. As to this problem, Yamashita (1989) developed approximation algorithm method and we can significantly clarify its characteristics. One of the remaining challenges is a sequence analysis among nodes of the fuzzy graph. This paper proposes a new index “fuzzy core index” to represent the importance of each node in sequence analysis. At first, we introduce the overview of the approximate analysis, and secondly we propose the new index for sequence analysis. Finally, we show the effectiveness of the proposed index through case study.