Clique
In graph theory, a clique is a subset of vertices in a graph where every pair of vertices is connected by an edge
In graph theory, a clique is a subset of vertices in a graph where every pair of vertices is connected by an edge. In simpler terms, it is a group of vertices that are all directly connected to each other. The size of a clique refers to the number of vertices it contains.
For example, let’s consider a graph with vertices A, B, C, D, and E. If every vertex in this graph is connected to every other vertex, then the graph contains a clique of size 5 because there is a fully connected group of 5 vertices.
Clique theory is commonly used in social network analysis to understand relationships and connections between individuals or entities. For instance, in a social network, a clique could represent a group of friends who are all connected to each other.
Clique can also be defined in the context of computational complexity theory. The maximal clique problem is the problem of finding the largest clique in a given graph, while the maximum clique problem is the problem of finding a clique of maximum size in a graph. Both of these problems are known to be computationally hard and are commonly studied in algorithms and computer science research.
In summary, a clique is a set of vertices in a graph where each pair of vertices is directly connected. It has various applications in graph theory, social network analysis, and computational complexity theory.
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