This thesis describes the importance and issues related to finding cliques in graphs. In addition to that, we mentioned some known ideas and algorithms for finding cliques. Our algorithm transforms the problem written in a graph into a geometrical problem in Euclidean space and finds a sphere that well-describes the vertices that belong to the clique. This way we find the pseudo-clique or seed of the clique if the former was not accomplished. After stating the mathematical terms necessary for understanding this thesis, we present an algorithm that finds a sphere in Euclidean space that well-describes the vertices belonging to a clique. The algorithm was conducted on random graphs of size 2000 with different edge probabilities and different clique sizes. All of the graphs have a previously set clique that is significantly larger than expected. For bigger cliques, a pseudo-clique was successfully found while in other cases seed of the clique was successfully found. Results show the huge potential for this kind of approach and we can say that the algorithm has shown success in finding the given clique whose size is significantly larger than the expected clique size. Shown algorithm has exceptionally good time performance with polynomial complexity