CLIQUE DETECTION FOR NONDIRECTED GRAPHS - 2 NEW ALGORITHMS

Making use of special tree search algorithms the present paper describes two new methods for determining all maximal complete subgraphs (cliques) of a finite nondirected graph. In both methods the blockwise generation of all cliques induces characteristic properties, which guarantee an efficient calculation of special clique subsets, especially the set of all cliques of maximal length. Moreover, by their structure both algorithms allow to calculate the complete clique set by parallel processing. The algorithms have been tested for many series of characteristic graphs and compared with the algorithm of Bron-Kerbosch (Algorithm 457 of CACM) the most efficient algorithm which is known to the authors. © 1979 Springer-Verlag.