The J. Kerbosch algorithm is a well-known method in computer science for finding all maximal cliques in an undirected graph. A maximal clique is a subset of vertices that forms a complete subgraph, meaning every pair of vertices in the subset is connected by an edge. The algorithm is efficient and often used in various applications, including social network analysis and bioinformatics. Developed by C. Erdős and A. Rényi, the J. Kerbosch algorithm employs a recursive backtracking approach. It systematically explores potential cliques and uses pruning techniques to eliminate non-promising candidates, making it effective for large graphs. This algorithm is significant in graph theory and combinatorial optimization.