Correlation mining is recognized as one of the most important data mining task for its capability to identify underlying dependencies between objects. And day by day data mining techniques are being increasingly applied to non-traditional domains, existing approaches for finding frequent itemsets and association rules to obtain knowledge from large volume of data, cannot be used as they cannot model the requirement of these domains. The graph modeling based data mining techniques are advantageous due to its capability of modeling various real life complex scenarios. Therefore, we have focused on graph databases. It has a wide range of application domains but existing works either find structural similarity based correlation or correlation with a specific graph. In this thesis we have proposed a new method of finding the underlying correlations among graphs in a graph database with a new graph correlation measure gConfidence. At first some necessary terminologies and some related works have been discussed, then provided some scenarios which motivated us in doing such work, then introduced our new measure along with some of its properties and proved its downward closure pruning capability. We have also provided a lemma and proved it, then we have introduced our correlation mining algorithm and analyzed its performance and found it scalable in terms of running time and memory usage, the algorithm is faster enough in mining correlation with graph databases having various number of graphs, various graph density and various threshold values. We have compared its performance with other existing graph correlation mining algorithms and found more than two times improvement on speed in mining correlation. Finally, we have illustrated some application scenarios and some application domains where our algorithm can be applied.