## 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:

- Suppose that G has n vertices.
- Find a vertex v of the smallest possible degree in G.
- If the degree of v is n − 1, stop; G is a clique, so the largest clique in G has size n.
- 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.