# Algorithm 457: finding all cliques of an undirected graph

@article{Bron1973Algorithm4F, title={Algorithm 457: finding all cliques of an undirected graph}, author={C. Bron and J. Kerbosch}, journal={Communications of The ACM}, year={1973}, volume={16}, pages={575-577} }

Description bttroductian. [...] Key Method The first version is a straightforward implementation of the basic algorithm. It is mainly presented to illustrate the method used. This version generates cliques in alphabetic (lexicographic) order. The second version is derived from the first and generates cliques in a rather unpredictable order in an attempt to minimize the number of branches to be traversed. Expand

#### 2,095 Citations

Listing all maximal cliques in large graphs on vertex-centric model

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- 2019

New efficient distributed algorithms for maximal clique enumerating based on the vertex-centric model using the BK algorithm principle are proposed and can effectively process a variety of large real-world and computer-generated graphs and scale well with increasing the dataset size and the number of nodes in the cluster. Expand

Comparison of Clique-Listing Algorithms

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- MSV/AMCS
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Five cliqueor MIS-listing algorithms are compared, and variations of the Bron and Kerbosch algorithm appear to be the fastest for random graphs and a type of graph which arises in physical mapping of genomes. Expand

A New Approach and Faster Exact Methods for the Maximum Common Subgraph Problem

- Computer Science
- COCOON
- 2005

In this paper a new algorithm, termed “clique branching,” is proposed that exploits a special structure inherent in the association graph that contains a large number of naturally-ordered cliques that are present in the Association graph’s complement. Expand

A linear time algorithm for maximal clique enumeration in large sparse graphs

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- Inf. Process. Lett.
- 2017

This paper proposes a linear time algorithm, CM-Constructor (Candidate Map Constructor), for maximal clique enumeration in large sparse graphs which generates a novel data structure called candidate map as result. Expand

A new decomposition technique for maximal clique enumeration for sparse graphs

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Using a new decomposition technique, two output sensitive algorithms for the maximal clique enumeration problem are presented, one of which has enumeration time depending on the degeneracy and the maximum degree and the other which only requires memory polynomial inThe degeneracy of the graph. Expand

Finding a Summary for All Maximal Cliques

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- 2021 IEEE 37th International Conference on Data Engineering (ICDE)
- 2021

The proposed method can reduce the number of bound calculations by 3 ∼ 5 orders of magnitude, and each run of the algorithm can be up to 2.x times faster than the state-of-the-art algorithm while still keeping the summary concise. Expand

Common subgraph isomorphism detection by backtracking search

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- 2004

An improved backtracking algorithm for CSI is proposed, which differs from its predecessors by better search strategy and is therefore more efficient and found that the new algorithm outperforms the traditional maximal clique approach by orders of magnitude in computational time. Expand

An Algorithm for Finding Maximal Common Subtopologies in a Set of Protein Structures

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A new suitable representation of the secondary structure topology of a protein by an undirected labeled graph is described and a new fast algorithm is developed that finds all common subtopologies in a set of protein structures. Expand

An Improved Upper Bound on Maximal Clique Listing via Rectangular Fast Matrix Multiplication

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Improve the asymptotics for the exploration of the same RS-tree by grouping the offsprings’ computation even further and rely on rectangular fast matrix multiplication in order to compute all children of n^2$$n2 nodes in one single shot. Expand

An Effective Algorithm for Extracting Maximal Bipartite Cliques

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The proposed algorithm adds the minimal number of edges that are required to convert all maximal bipartite cliques to maximal cliques, which is accurate, efficient, effective, and applicable to real world graphs more than the traditional algorithm. Expand

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