In this paper, we present a new metric distance for comparing two large graphs to find similarities and differences between them based on one of the most important graph structural properties, which is Node Adjacency Information, for all vertices in the graph. Then, we defined a new function and some parameters to find the distance of two large graphs using different neighbors of vertices. There are some methods which they focused on the other features of graphs to obtain the distance between them, but some of them are Node Correspondence which means their node set have the same size. However, in this paper, we introduce a new method which can find the distance between two large graphs with different size of node set.