Graphs are widely used in large scale social network analysis. Graph mining increasingly important in modelling complicated structures such as circuits, images, web, biological networks and social networks. The major problems occur in this graph mining are computational efficiency (CE) and frequent subgraph mining (FSM). Computational Efficiency describes the extent to which the time, effort or efficiency which use computing technology in information processing. Frequent Sub graph Mining is the mechanism of candidate generation without duplicates. FSM faces the problem on counting the instances of the patterns in the dataset and counting of instances for graphs. The main objective of this project is to address CE and FSM problems. The paper cited in the reference proposes an algorithm called Mirage algorithm to solve queries using subgraph mining. The proposed work focuses on enhancing An Iterative Map Reduce based Frequent Subgraph Mining Algorithm (MIRAGE) to consider optimum computational efficiency. The test data to be considered for this mining algorithm can be from any domains such as medical, text and social data’s (twitter). The major contributions are: an iterative MapReduce based frequent sub graph mining algorithm called MIRAGE used to address the frequent sub graph mining problem.