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ABSTRACT Knowledge discovery in database (KDD) is the process of identifying a valid, potentially useful and ultimately understandable structure in data. Data mining is a step in the KDD process concerned with the algorithmic means by which patterns or structures are enumerated from the data under acceptable computational efficiency limitations. Thus, the structures what are the outcome of the data mining process must meet certain conditions so that these can be considered as knowledge. Data Mining is also concerned with the extraction of patterns from the data. Data mining is the exploration and analysis of large data sets, in order to discover meaningful patterns and rules. In other words, Data mining is defined as the nontrivial process of identifying valid, novel, potentially useful, and ultimately understandable patterns in data. The fundamental goal of data mining is the prediction and description. The relative emphasis of both prediction and description differ with respect to the underlying application and the technique. There are several data mining techniques fulfilling these objectives. In recent years, graph mining has attracted more research interest because of its broad application areas such as bioinformatics, cheminformatics, natural language processing etc. Since structure is represented by proper relations and a graph can easily represent relations, knowledge discovery from graph structured data poses a general problem for mining from structured data. The domain of graph mining includes scalable pattern mining techniques, indexing and searching graph databases, clustering, classification and various other applications and exploration technologies. Graph mining focuses mainly on mining complicated patterns from graph databases A graph is a set of nodes and links (or vertices and edges), where the nodes and/or links can have arbitrary labels, and the links can be directed or undirected (implying an ordered or unordered relation). Therefore, mining graph data, sometimes called graph-based data mining (GDM), is the extraction of novel and useful knowledge from a graph representation of data. Two major classification of GDM are frequent subgraph mining and graph-based relational learning. Within the graph, the problem of finding frequent patterns becomes that of mining subgraph which occurs frequently over the entire set of graphs. Several approaches exist based on the task of identifying frequently occurring subgraphs. That is, those subgraph meeting a minimum level of support. In the advents of the existing research, several clever algorithms for frequent subgraph mining have been developed. All the algorithms developed are originally for frequent item set mining. The fundamental frequent pattern algorithms are classified into three types as follows: 1. Candidate generation approach (E.g. Apriori algorithm) 2. Without candidate generation approach (E.g. FP-growth algorithm) 3. Vertical layout approach (E.g. Eclat algorithm) All the above methods are used to discover the frequent pattern only in a graph dataset. There is no high amount of research in the area of applying ranking over the subgraphs. The frequent subgraphs with similar patterns have to be compulsorily classified under the ranking. This means, if similar pattern exists, then ranking of them will lead to a solution of placing them in an appropriate order for proceding a graph performance. The ranking plays an important role in many graph applications. The main aim of this research work is to devise the new ranking technique for the subgraphs and apply the ranking method to various frequent subgraph algorithms. In order to establish the ranking of subgraphs, this research work has proposed four main stages of the algorithms and the overall algorithm is related to association rule mining. The proposed algorithm can be applied to the methods which includes either candidate generation approach or without candidate generation approach. The first stage proposes the evaluation of lift measure. Before that, the rules are extracted from the mined frequent subgraphs. The lift values are then calculated for every rule. The lift measure is the statistically proved one, the nature of which is to exemplify the relation between the two quantities. The second stage of the algorithm proposes the Modified form of the Discounted Cumulative Gain (MDCG). This new form of Discounted Cumulative Gain is obtained by using lift measure. The MDCG and the corresponding ideal ordering of MDCG (IMDCG) are evaluated at this stage. Third stage is proposed by an innovative method to calculate the new normalized measure called “Graphgain (GG)” using the lift value. The advantage of the lift measure is used to obtain the GG. The proposed ranking of subgraphs technique is constructed from the existing normalized discounted cumulative gain (nDCG). The performance of the proposed algorithm is studied with retail dataset. The proposed algorithm performs better than Apriori and FP-Growth algorithms with the additional phase of ranking. The final stage of the algorithm presents efficient technique for ranking the mined subgraphs. This research work has a simple and efficient method of ranking subgraphs so that, this technique can be applied to any one of the existing subgraph mining algorithms. This thesis presents an efficient ranking method in which the ranking is based on the unique values of GG. The performance of the proposed algorithm is studied by using synthetic and chemical dataset. The proposed algorithm is also compared with Apriori, FP-Growth methods.