Graph mining is a well-established research field, and lately it has drawn in considerable research communities. It allows to process, analyze, and discover significant knowledge from graph data. In graph mining, one of the most challenging tasks is frequent subgraph mining (FSM). FSM consists of applying the data mining algorithms to extract interesting, unexpected, and useful graph patterns from the graphs. 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. These techniques can be classed into two primary categories: (i) a priori-based FSM approaches and (ii) pattern growth-based FSM approaches. In both of these categories, an extensive research work is available. 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. Thus, the aim of this research is to make do with the challenges of enormous FSPs, avoid duplicate discovery of FSPs, and use the ranking for such patterns. Therefore, to address these challenges a new FSM framework A RAnked Frequent pattern-growth Framework (A-RAFF) is suggested. Consequently, A-RAFF provides an efficacious answer to these challenges through the initiation of a new ranking measure called FSP-Rank. The proposed ranking measure FSP-Rank effectively reduced the duplicate and enormous frequent patterns. The effectiveness of the techniques proposed in this study is validated by extensive experimental analysis using different benchmark and synthetic graph datasets. Our experiments have consistently demonstrated the promising empirical results, thus confirming the superiority and practical feasibility of the proposed FSM framework.