Frequent subgraph mining (FSM) is a fundamental problem in graph analysis with wide-ranging applications in bioinformatics, social network analysis, cybersecurity, and cheminformatics. This paper presents efficient algorithms for FSM in complex networks, addressing the computational challenges posed by large-scale graph data. Traditional approaches often suffer from scalability issues due to the combinatorial explosion of subgraph candidates. To mitigate these challenges, we propose an optimized FSM framework leveraging advanced pruning techniques, graph compression, and parallel computing. Our approach incorporates pattern-growth strategies with heuristic search methods to improve computational efficiency while maintaining accuracy. We evaluate our proposed algorithms on benchmark datasets, demonstrating significant performance gains over existing methods in terms of runtime and memory consumption. Additionally, we explore real-world applications, such as detecting anomalous patterns in cybersecurity networks, identifying molecular structures in drug discovery, and analyzing connectivity patterns in social networks. The results underscore the potential of efficient FSM algorithms in extracting meaningful insights from complex graph data. This research contributes to the advancement of graph mining techniques, providing a scalable and effective solution for large-scale network analysis. Future work will explore deep learning-based enhancements to further optimize FSM in dynamic and evolving graph structures.