## What is clique in graph example?

It is an example of median graph, and is associated with a median algebra on the cliques of a graph: the median m(A,B,C) of three cliques A, B, and C is the clique whose vertices belong to at least two of the cliques A, B, and C. The clique-sum is a method for combining two graphs by merging them along a shared clique.

## How do you find the clique on a graph?

To find a clique of G:

1. Suppose that G has n vertices.
2. Find a vertex v of the smallest possible degree in G.
3. If the degree of v is n − 1, stop; G is a clique, so the largest clique in G has size n.
4. Otherwise, remove v and all of its edges from G. Find the largest clique in the smaller graph.

What is clique in respect to undirected graph?

A clique is a subset of vertices of an undirected graph G such that every two distinct vertices in the clique are adjacent; that is, its induced subgraph is complete. Cliques are one of the basic concepts of graph theory and are used in many other mathematical problems and constructions on graphs.

Is a clique a complete graph?

A complete graph is often called a clique. The size of the largest clique that can be made up of edges and vertices of G is called the clique number of G.

### Is clique a complete graph?

A clique in a graph G is a complete subgraph of G. That is, it is a subset K of the vertices such that every two vertices in K are the two endpoints of an edge in G. A maximal clique is a clique to which no more vertices can be added.

### Is an edge a clique?

The edge-clique graphK(G) of a graphG is that graph whose vertices correspond to the edges ofG and where two vertices ofK(G) are adjacent whenever the corresponding edges ofG belong to a common clique. An algorithm is provided for determining whether a graph is an edge-clique graph.

Is clique a NP?

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.

What was the purpose of the clique?

Cliques at work can be a means of self-preservation. Employees have a group of people that supports them and validates their perceptions. They provide the safety that people need when they’re feeling vulnerable.

## What is the best definition of clique?

: a narrow exclusive circle or group of persons especially : one held together by common interests, views, or purposes high school cliques.

## What is clique in algorithm?

Algorithms clique A clique is a subset of vertices of an undirected graph G such that every two distinct vertices in the clique are adjacent; that is, its induced subgraph is complete. Cliques are one of the basic concepts of graph theory and are used in many other mathematical problems and constructions on graphs.

What is the definition of a clique in graph theory?

A clique is a subset of vertices of an undirected graph G such that every two distinct vertices in the clique are adjacent; that is, its induced subgraph is complete. Cliques are one of the basic concepts of graph theory and are used in many other mathematical problems and constructions on graphs.

How is a clique complex related to a simplex graph?

The clique complex of a graph G is an abstract simplicial complex X(G) with a simplex for every clique in G. A simplex graph is an undirected graph κ(G) with a vertex for every clique in a graph G and an edge connecting two cliques that differ by a single vertex.

### How do you find a maximal clique in a graph?

A single maximal clique can be found by a straightforward greedy algorithm. Starting with an arbitrary clique (for instance, any single vertex or even the empty set), grow the current clique one vertex at a time by looping through the graph’s remaining vertices.

### Which is the minimum number of cliques needed to cover all the edges?

Mathematics. The intersection number of a graph is the minimum number of cliques needed to cover all the graph’s edges. The clique graph of a graph is the intersection graph of its maximal cliques. Closely related concepts to complete subgraphs are subdivisions of complete graphs and complete graph minors.