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In topological spaces, which are branches of pure mathematics, are difficult to find, the significance of this paper is to find some in graph theory via some topological space concepts, we introduced some well-known concepts in topology and related them to a graph such as (graph interior, graph closure, graph exterior, graph boundary and graph limit point). We study a characterization and relationships between them and present some results and theorems about this notions. In this work includes all Species graphs. [ABSTRACT FROM AUTHOR]