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In this paper, a new topological approach for studying an integer sequence constructed from Logistic mapping is proposed. By evenly segmenting [0,1] into N non-overlapping subintervals which is marked as , representing the nodes identities, a network is constructed for analysis. Wherein the undirected edges symbolize their relation of adjacency in an integer sequence obtained from the Logistic mapping and the top integral function. By observation, we find that nodes’ degree changes with different values of instead of the initial value—X0, and the degree distribution presents the characteristics of scale free network, presenting power law distribution. The results presented in this paper provide some insight into degree distribution of the network constructed from integer sequence that may help better understanding of the nature of Logistic mapping.