Bron-Kerbosch maximal clique finding algorithm
[MC] = MAXIMALCLIQUES(A,V_STR) Given a graph's boolean adjacency matrix, A, find all maximal cliques on A using the Bron-Kerbosch algorithm in a recursive manner.
V_STR is an optional input string with the version of the Bron-Kerbosch algorithm to be used (either 'v1' or 'v2'). Version 2 is faster (and default), and version 1 is included for posterity.
The output matrix MC contains the maximal cliques in its columns.
Note: This function can be used to compute the maximal independent sets of a graph A by providing the complement of A as the input graph.
Note: This function can be used to compute the maximal matchings of a graph A by providing the complement of the line graph of A as the input graph.
Ref: Bron, Coen and Kerbosch, Joep, "Algorithm 457: finding all cliques of an undirected graph", Communications of the ACM, vol. 16, no. 9, pp: 575–577, September 1973.
Ref: Cazals, F. and Karande, C., "A note on the problem of reporting maximal cliques", Theoretical Computer Science (Elsevier), vol. 407, no. 1-3, pp: 564-568, November 2008.
Cite As
Jeffrey Wildman (2024). Bron-Kerbosch maximal clique finding algorithm (https://www.mathworks.com/matlabcentral/fileexchange/30413-bron-kerbosch-maximal-clique-finding-algorithm), MATLAB Central File Exchange. Retrieved .
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Acknowledgements
Inspired by: Maximal Cliques, Bron-Kerbosch maximal independent set and maximal clique algorithms, Maximal Independent Sets using JGraphT
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