subgraphs are used to model social cliques, groups of people who all know each other. used graphs to model social networks, and adapted the social science terminology to graph theory. They were the first to call complete subgraphs "cliques". The first algorithm for solving the clique problem is that of , who were motivated by the sociological application. Social science researchers have also defined various other types of cliques and maximal cliques in social network, "cohesive subgroups" of people or actors in the network all of whom share one of several different kinds of connectivity relation. Many of these generalized notions of cliques can also be found by constructing an undirected graph whose edges represent related pairs of actors from the social network, and then applying an algorithm for the clique problem to this graph. Since the work of Harary and Ross, many others have devised algorithms for various versions of the clique problem. In the 1970s, researchers began studying these algorithms from the point of view of worst-case analysis. See, for instance, , an early work on the worst-case complexity of the maximum clique problem. Also in the 1970s, beginning with the work of and , researchers began using the theory of NP-completeness and related intractability results to provide a mathematical explanation for the perceived difficulty of the clique problem. In the 1990s, a breakthrough series of papers beginning with and reported in The New York Times, showed that (assuming P ≠ NP) it is not even possible to approximate the problem accurately and efficiently. Clique-finding algorithms have been used in chemistry, to find chemicals that match a target structure and to model molecular docking and the binding sites of chemical reactions. They can also be used to find similar structures within different molecules. In these applications, one forms a graph in which each vertex represents a matched pair of atoms, one from each of two molecules. Two vertices are connected by an edge if the matches that they represent are compatible with each other. Being compatible may mean, for instance, that the distances between the atoms within the two molecules are approximately equal, to within some given tolerance. A clique in this graph represents a set of matched pairs of atoms in which all the matches are compatible with each other. A special case of this method is the use of the modular product of graphs to reduce