Bron-Kerbosch Algorithm

The Bron-Kerbosch algorithm is an enumeration algorithm for finding all maximal cliques in an undirected graph, listing every subset of vertices in which each pair is connected by an edge and to which no further vertex can be added while preserving that property. It was designed by the Dutch scientists Coenraad Bron and Joep Kerbosch, who published its description in 1973. Although other clique-finding algorithms have theoretically better running times on inputs with few maximal independent sets, the Bron-Kerbosch algorithm and its later refinements are frequently reported as more efficient in practice, and it is widely used in application areas such as computational chemistry.