Title: An Algorithm for Finding All Maximal Cliques in a Graph Sergiy Butenko Department of Industrial Engineering Texas A&M University 236E Zachry Engineering Center College Station, TX 77843-3131 Email: butenko@tamu.edu Web page: http://ie.tamu.edu/people/faculty/butenko/ Abstract: An algorithm for finding all maximal cliques in an arbitrary graph is presented. The proposed algorithm outperforms other existing approaches on large sparce graphs. This work was motivated by applications in computational biochemistry.