Graph mining is a well-established research field and lately it has drawn considerable attention of research communities. It allows to process, analyze, and discover significant knowledge from graph data. Graph mining has been highly motivated by the enormous number of applications. Such applications include Chemoinformatics, Bioinformatics, and societal networks. In graph mining, one of the most challenging tasks is Frequent Subgraph Mining (FSM). FSM has been applied to many domains, such as graphical data management and knowledge discovery, social network analysis, Bioinformatics, and security. In this context, a large number of techniques have been suggested to deal with the graph data. However, FSM approaches are facing some challenges, including enormous numbers of Frequent Subgraph Patterns (FSPs); no suitable mechanism for applying ranking at the appropriate level during the discovery process of the FSPs; extraction of repetitive and duplicate FSPs; user involvement in supplying the support threshold value; large number of subgraph candidate generation; and there exists no specialized scheme to decide the discovered FSPs are optimized patterns as well. Thus, the aim of this research is to make cope with the challenges of enormous FSPs, avoid duplicate discovery of FSPs, use the ranking for the discovered FSPs, and to suggest an optimization strategy to illustrate an association between the frequent and the optimized subgraph patterns. The exploration of this association will further help to decide on the FSPs as optimized FSPs. Therefore, to address the aforementioned challenges a new FSM framework A RAnked Frequent pattern-growth Framework (A-RAFF) is developed. The proposed FSM framework, A-RAFF, provides an efficient answer to these challenges through the initiation of a new ranking measure called FSP-Rank. The proposed ranking measure FSP-Rank, based on the characteristics of the FSPs, effectively reduced the duplicate and enormous FSPs. Moreover, in this study, we have investigated the association between FSPs and optimized subgraph using a Particle Swarm Optimization technique. The effectiveness of the techniques proposed in the dissertation is validated by extensive experimental analysis using different benchmarks, both real and synthetic graph datasets. Finally, our experiments have consistently demonstrated promising empirical results, thus confirming the superiority and practical feasibility of the proposed FSM framework.