Description: A clique in a graph is a subset of vertices that forms a complete subgraph, meaning every pair of vertices within this subset is connected by an edge. This total connectivity property among the vertices distinguishes a clique from other subsets of vertices. Cliques are fundamental in graph theory as they allow for a deeper analysis of the structure and relationships within a graph. A clique can vary in size, from a single vertex to the total number of vertices in the graph, and is classified into maximal cliques (which cannot be expanded without losing the clique property) and maximum cliques (which are the largest cliques in terms of the number of vertices). Identifying cliques in a graph has implications in various fields, such as network optimization, computational biology, and social network analysis, where understanding how elements group and interact is crucial. In summary, cliques are essential components in graph theory that help decompose and understand the complexity of relationships in interconnected data structures.
