Power laws play a crucial role in understanding the structural and functional properties of real-world graphs, influencing various aspects of graph mining and query processing. This paper explores the prevalence of power-law distributions in large-scale graph structures and their implications for graph query analysis. We investigate techniques for efficiently mining graphs that exhibit power-law characteristics, leveraging these distributions to optimize query performance and scalability. Our study presents a comprehensive review of existing methodologies for detecting power-law behavior in graphs, highlighting their impact on graph traversal, indexing, and query execution. We also examine algorithmic optimizations tailored for power-law graphs, including degree-based indexing, community-aware search techniques, and efficient subgraph matching approaches. Furthermore, we discuss the applications of power-law principles in diverse domains such as social network analysis, bioinformatics, and knowledge graphs. Through empirical analysis on real-world datasets, we demonstrate how power-law-aware techniques improve query efficiency and reduce computational complexity in large graph databases. The findings of this study offer valuable insights into the interplay between graph topology and query optimization, paving the way for enhanced graph mining frameworks. Our work contributes to the development of more scalable and intelligent graph query processing systems, with broad implications for data-driven decision-making.