Graph Isomorphism is a one-to-one and on-to mapping between two graphs so that the Properties of each vertex on one graph correspond to the properties of a vertex on the other graph. The graph isomorphism problem is a computational problem of determining whether two finite graphs are isomorphic or not. It is one of the small numbers of a problems belonging to NP neither known to be solvable in polynomial time nor NP complete. In this paper, I proposed an algorithm that determines whether two finite graphs are isomorphic or not. Keywords: Direct Path Set Of Vertex, Set Intersection, Adjacency matrix, Null Set.