Bron–Kerbosch algorithm

In <a href="/facts/Computer_science/lN3pEyPz">computer science</a>, the Bron–Kerbosch algorithm is an <a href="/facts/Enumeration_algorithm/fLMKo24Y">enumeration algorithm</a> for finding all maximal <a href="/facts/Clique_(graph_theory)/XK9ppLz5">cliques</a> in an undirected <a href="/facts/Graph_(discrete_mathematics)/kw3eIBUe">graph</a>. That is, it lists all <a href="/facts/Subset/SJGERmbA">subsets</a> of vertices with the two properties that each pair of vertices in one of the listed subsets is connected by an edge, and no listed subset can have any additional vertices added to it while preserving its <a href="/facts/Complete_graph/AYD6hUqI">complete connectivity</a>. The Bron–Kerbosch algorithm was designed by <a href="/facts/Netherlands/y8xn5stT">Dutch</a> scientists <a href="/facts/Coenraad_Bron/xSx9B3VA">Coenraad Bron</a> and Joep Kerbosch, who published its description in 1973. 
Although other algorithms for solving the <a href="/facts/Clique_problem/cVVBNP08">clique problem</a> have running times that are, in theory, better on inputs that have few maximal independent sets, the Bron–Kerbosch algorithm and subsequent improvements to it are frequently reported as being more efficient in practice than the alternatives. It is well-known and widely used in application areas of <a href="/facts/Graph_algorithm/g3uenNkc">graph algorithms</a> such as <a href="/facts/Computational_chemistry/KyuCgRV3">computational chemistry</a>.
A contemporaneous algorithm of Akkoyunlu (1973), although presented in different terms, can be viewed as being the same as the Bron–Kerbosch algorithm, as it generates the same search tree.

Bron–Kerbosch algorithm open-in-new

Bron–Kerbosch algorithm