This thesis explores graphlet counting algorithms, which are crucial for understanding the structural principles of complex networks such as bioinformatics, social networks, and network model evaluation. Counting graphlets in large networks is computationally challenging due to the combinatorial explosion of possibilities, particularly for larger graphlet sizes. To address this, we focus on clique graphlets, fully connected subgraphs, which reveal critical patterns in areas like protein structure analysis, social network modeling, community detection, and spam detection. Counting k-cliques (subgraphs with $k$ nodes) becomes infeasible for large datasets and high $k$ values. Existing exact and approximate algorithms struggle with large $k$, often failing when $k$ exceeds 10. To tackle these limitations, we propose BDAC (Boundary-Driven Approximations of K-Cliques), a novel algorithm that efficiently approximates k-clique counts using classical extremal graph theorems. BDAC uniquely provides lower and upper bounds for k-clique counts at both local (per vertex) and global levels, making it particularly suited for large, dense graphs with high $k$ values. Unlike existing methods, the algorithm's complexity remains unaffected by the value of $k$. We validate BDAC's efficiency and scalability through extensive comparisons with leading algorithms on diverse datasets, spanning k values from minor (e.g., 8) to large (e.g., 50). Parallelization techniques enhance its performance, making it highly scalable for analyzing large and dense networks. BDAC offers a significant advancement in k-clique counting, enabling the analysis of previously considered computationally intractable networks.