1. A method for maximizing group membership comprising: updating by a processor a connectivity count of each vertex in a graph after removing one vertex from said graph, wherein the connectivity count of a vertex is a number of neighbors connected to the vertex, said connectivity count stored in said memory; selecting by said processor a vertex with a least sum of connectivity counts of all its neighboring vertices from among all vertices having a same least connectivity count; removing by said processor said selected vertex from the graph; returning by said processor a grouping of interconnected vertices forming a clique when each vertex in said grouping is connected to each other vertex in said grouping; for a determination of said removed vertex having a connectivity count equaling zero, said processor returning a grouping consisting of the removed vertex with a connectivity count equaling zero and all its neighboring vertices, said neighboring vertices including any vertex removed in any previous iteration of the selecting and removing steps, said grouping forming a current eliminated clique; comparing by said processor a number of vertices in said current eliminated clique with a number of vertices in each previously eliminated and stored clique; and storing by said processor the current eliminated clique in said memory if the current eliminated clique has a size greater than a size of any of previously eliminated and stored clique.