Let G = (V, E) be a locally finite GRAPH, i.e. a GRAPH in which every vertex has finitely many adjacent vertices. In this paper, we associate a TOPOLOGY to G, called GRAPHic TOPOLOGY of G and we show that it is an Alexandro TOPOLOGY, i.e. a TOPOLOGY in which intersection of each family of open sets is open. Then we investigate some properties of this TOPOLOGY. Our motivation is to give an elementary step toward investigation of some properties of locally finite GRAPHs by their corresponding TOPOLOGY which we introduce in this paper.