Data mining analysis methods are increasingly being applied to data sets derived from science and engineering domains which represent various physical phenomena and objects. In many of data sets, a key requirement of effective analysis is the ability to capture the relational and geometric characteristics of the underlying entities and their relationships with vertices and edges, which provide a natural method to represent such data sets.In Apriori-based graph mining, to determine candidate sub graphs from a huge number of generated adjacency matrices, where the dominating factor is, the overall graph mining performance because it requires to perform many graph isomorphism test . The pattern-growth approach is more flexible for the expansion of an existing graph.