Editing Clique (graph theory) (section)

==Applications==
The word "clique", in its graph-theoretic usage, arose from the work of {{harvtxt|Luce|Perry|1949}}, who used complete subgraphs to model [[clique]]s (groups of people who all know each other) in [[social network]]s. The same definition was used by {{harvtxt|Festinger|1949}} in an article using less technical terms. Both works deal with uncovering cliques in a social network using matrices. For continued efforts to model social cliques graph-theoretically, see e.g. {{harvtxt|Alba|1973}}, {{harvtxt|Peay|1974}}, and {{harvtxt|Doreian|Woodard|1994}}.

Many different problems from [[bioinformatics]] have been modeled using cliques. For instance, {{harvtxt|Ben-Dor|Shamir|Yakhini|1999}} model the problem of clustering [[gene expression]] data as one of finding the minimum number of changes needed to transform a graph describing the data into a graph formed as the disjoint union of cliques; {{harvtxt|Tanay|Sharan|Shamir|2002}} discuss a similar [[biclustering]] problem for expression data in which the clusters are required to be cliques. {{harvtxt|Sugihara|1984}} uses cliques to model [[ecological niche]]s in [[food chain|food webs]]. {{harvtxt|Day|Sankoff|1986}} describe the problem of inferring [[evolutionary tree]]s as one of finding maximum cliques in a graph that has as its vertices characteristics of the species, where two vertices share an edge if there exists a [[perfect phylogeny]] combining those two characters. {{harvtxt|Samudrala|Moult|1998}} model [[protein structure prediction]] as a problem of finding cliques in a graph whose vertices represent positions of subunits of the protein. And by searching for cliques in a [[protein–protein interaction]] network, {{harvtxt|Spirin|Mirny|2003}} found clusters of proteins that interact closely with each other and have few interactions with proteins outside the cluster. [[Power graph analysis]] is a method for simplifying complex biological networks by finding cliques and related structures in these networks.

In [[electrical engineering]], {{harvtxt|Prihar|1956}} uses cliques to analyze communications networks, and {{harvtxt|Paull|Unger|1959}} use them to design efficient circuits for computing partially specified Boolean functions. Cliques have also been used in [[automatic test pattern generation]]: a large clique in an incompatibility graph of possible faults provides a lower bound on the size of a test set.<ref>{{harvtxt|Hamzaoglu|Patel|1998}}.</ref> {{harvtxt|Cong|Smith|1993}} describe an application of cliques in finding a hierarchical partition of an electronic circuit into smaller subunits.

In [[chemistry]], {{harvtxt|Rhodes|Willett|Calvet|Dunbar|2003}} use cliques to describe chemicals in a [[chemical database]] that have a high degree of similarity with a target structure. {{harvtxt|Kuhl|Crippen|Friesen|1983}} use cliques to model the positions in which two chemicals will bind to each other.