Frequent subgraph mining (FSM) is one of the most challenging tasks in graph mining. FSM consists of applying the data mining algorithms to extract interesting, unexpected, and useful graph patterns from the graphs. It also aspires to offer a richer apprehension of the given graph data. 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, with the objective to extract the frequently occurring graph patterns. Such patterns are called frequent subgraph patterns (FSPs). FSPs are extracted using the traditional support threshold parameter. However, there exists no specialized scheme to decide the discovered FSPs are optimized as well. Thus, the aim of this paper is to suggest an optimization strategy to uncover the association between the frequent and the optimized subgraph patterns. For exploring the existence of the potential association between the FSPs and the optimized subgraph, a Particle Swarm Optimization technique is suggested. This relationship will be very handy to reduce the FSPs, by choosing those FSPs which were also discovered as optimized FSPs. Different experiments are performed using benchmark graph data sets to validate the existence of the aforementioned relationship between the optimized and the frequent FSPs.