These regions of high link density are often referred to as cliques, hubs, compartments, cohesive sub-groups, or modules ... Within food webs, especially in aquatic systems, nestedness appears to be related to body size because the diets of smaller predators tend to be nested subsets of those of larger predators ( Woodward & Warren 2007 ; YvonDurocher et al.

Cliques have also been studied in computer science: finding whether there is a clique of a given size in a graph ( the clique problem ) is NP-complete, but despite this hardness result many algorithms for finding cliques have been studied.

The perfect graph theorem states that the complement of a perfect graph is perfect ; equivalently, in a perfect graph, the size of the maximum independent set equals the minimum number of cliques in a clique cover.

The k-trees are the chordal graphs in which all maximal cliques and all maximal clique separators have the same size.

For a node labeled 1, the maximum clique is the union of the cliques computed for that node's children, and has size equal to the sum of the children's clique sizes.

After the Washington Naval Conference of 1921-22, where Japan agreed to keep the size of its fleet smaller than that of the United Kingdom and the United States, the Imperial Japanese Navy became divided into the mutually hostile Fleet Faction and Treaty Faction political cliques.

* The Erdős – Faber – Lovász conjecture on coloring unions of cliques.

* The Erdős – Faber – Lovász conjecture is another unproven statement relating graph coloring to cliques.

Instead of cliques, if the same question is asked for complete multi-partite graphs, the answer is given by the Erdős – Stone theorem.

An instance of the Erdős – Faber – Lovász conjecture: a graph formed from four cliques of four vertices each, any two of which intersect in a single vertex, can be four-colored.

The graph of the Erdős – Faber – Lovász conjecture may be represented as an intersection graph of sets: to each vertex of the graph, correspond the set of the cliques containing that vertex, and connect any two vertices by an edge whenever their corresponding sets have a nonempty intersection.

The adoption of school or district-wide uniform policies ( or, alternatively, " standardized dress codes " – which are not as rigid as school uniform requirements, but allow some leeway within set parameters ) has been motivated by a need to counter " gang clothing " ( or, in the alternative, the pressure for families to purchase upscale-label clothing to avoid their children being ignored by " fashion cliques "), as well as to improve morale and school discipline.

Nevertheless, many algorithms for computing cliques have been developed, either running in exponential time ( such as the Bron – Kerbosch algorithm ) or specialized to graph families such as planar graphs or perfect graphs for which the problem can be solved in polynomial time.

* Floater – Similar to a Liaison ; closely associated with multiple cliques

They believe that children need the 2 – 3 months off to relax and also to take a break from other childhood stresses associated with school such as peer pressure, cliques, bullying, and the pressure of heavy loads of schoolwork and homework.

To prove the perfect graph theorem, Lovász used an operation of replacing vertices in a graph by cliques ; it was already known to Berge that, if a graph is perfect, the graph formed by this replacement process is also perfect.

In the formulation of coloring graphs formed by unions of cliques, Hindman's result shows that the conjecture is true whenever at most ten of the cliques contain a vertex that belongs to three or more cliques.

It may also become harder to defend political privacy, where extreme views and strong challenges to the dominant political system are beginning to threaten the power of dominant cliques in society-who tend to prefer in general a zero-accountability carceral state.

These problems are all hard: the clique decision problem is NP-complete ( one of Karp's 21 NP-complete problems ), the problem of finding the maximum clique is both fixed-parameter intractable and hard to approximate, and listing all maximal cliques may require exponential time as there exist graphs with exponentially many maximal cliques.

Several important classes of graphs may be defined by their cliques:

Despite the close relationship between maximum cliques and maximum independent sets in arbitrary graphs, the independent set and clique problems may be very different when restricted to special classes of graphs.

In order to do this, it may be necessary for some of the cliques to be single vertices.

More generally, a chordal graph can have only linearly many maximal cliques, while non-chordal graphs may have exponentially many.

Although similar cliques may re-emerge in adulthood in specific contexts characterized by large, undifferentiated, anonymous crowds, overall, cliques are a transitory social phase ( 159 ).

Girls do, however, tend to form cliques earlier ( 11 years old as compared to 13 or 14 among boys ), which may contribute to the greater popular salience of female cliques.

Male cliques, on the other hand tend to center around activities most of which occurred before the formation of the clique ( common examples include basketball and videogames ), and thus may draw less attention to the appearance of male cliques.

Finally, male cliques may have gone unnoticed because they often appear less exclusive toward the non-clique peer group members.

The characteristics of the distinct cliques within each demographic group also vary equally, although members of cliques in one crowd or demographic group may not perceive all of the distinctions in others ( see also crowds ).

Because adolescent females, on average, both report stronger feelings of group belonging and place greater importance on this feeling than do their male peers, girls who do not feel accepted may be more susceptible than equally excluded boys to forming and conforming to cliques based on shared maladaptive behavior.

Many of the effects on cliques composition described below may be largely attributed to crowd segregation.

This rule is intended to disestablish cliques or vendettas which may form and promote social interaction.

Mustafa I was reported to be mentally retarded or at least neurotic and was never more than a tool of court cliques at the Topkapı Palace.

* listing all maximal cliques ( cliques that cannot be enlarged )

He and Jiang Qing are still considered to be the two " major Counter-revolutionary cliques " blamed for the excesses of the Cultural Revolution.

In 1981, the government released their verdict: that Lin Biao must be held, along with Jiang Qing, as one of the two major " counter-revolutionary cliques " responsible for the excesses of the late 1960s.

These films are often set in or around high schools as this allows for many different social cliques to be shown.

* An interval graph is a graph whose maximal cliques can be ordered in such a way that, for each vertex v, the cliques containing v are consecutive in the ordering.

* A line graph is a graph whose edges can be covered by edge-disjoint cliques in such a way that each vertex belongs to exactly two of the cliques in the cover.

For instance, 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 ; discuss a similar biclustering problem for expression data in which the clusters are required to be cliques.

Bob Ellis wrote in Overland, ‘ What I think absorbs the reader in the deeply revelatory un-memoir Wild Amazement is ... Michael ’ s clear, almost hyper-real remembrance, as if experienced on a guided tour of a radiant, countercultural Disneyland, of a way of life, and a gravely joyous bohemia now gone, of how it was, and what a time it was, it really was, in Sydney in the sixties and seventies, in the Newcastle and the Journos ’ Club and the Push parties and the plans for a literary life .’ And in, Quadrant, Peter Corris wrote, ‘ Anyone interested in how contemporary Australian writing came to be the way it is, with its strengths and follies, its cliques and patrons, and the challenges it faces, will benefit from reading Wilding ’ s sensitive, sometimes bitchy, often funny and always intelligent tracing of his life ’ s trajectory .’ The Italian translation of Wild Amazement appeared in 2009.

These include the forests, k-trees ( maximal graphs with a given treewidth ), split graphs ( graphs that can be partitioned into a clique and an independent set ), block graphs ( graphs in which every biconnected component is a clique ), interval graphs ( graphs in which each vertex represents an interval of a line and each edge represents a nonempty intersection between two intervals ), trivially perfect graphs ( interval graphs for nested intervals ), threshold graphs ( graphs in which two vertices are adjacent when their total weight exceeds a numerical threshold ), windmill graphs ( formed by joining equal cliques at a common vertex ), and strongly chordal graphs ( chordal graphs in which every even cycle of length six or more has an odd chord ).

It is also of interest to consider the chromatic number of graphs formed as the union of cliques of vertices each, without restricting how big the intersections of pairs of cliques can be.