Journal ArticleDOI
The Enumeration of Maximal Cliques of Large Graphs
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An algorithm for enumerating maximal cliques (complete subgraphs) is proposed, which aims to deal with the difficulties caused by the size of the problem.Abstract:
An algorithm for enumerating maximal cliques (complete subgraphs) is proposed. The aim is to deal with the difficulties caused by the size of the problem.read more
Citations
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Book ChapterDOI
The maximum clique problem
TL;DR: A survey of results concerning algorithms, complexity, and applications of the maximum clique problem is presented and enumerative and exact algorithms, heuristics, and a variety of other proposed methods are discussed.
Journal ArticleDOI
Efficient sampling algorithm for estimating subgraph concentrations and detecting network motifs
TL;DR: A novel algorithm is presented that allows estimation of subgraph concentrations and detection of network motifs at a runtime that is asymptotically independent of the network size and can be applied to estimate the concentrations of larger subgraphs in larger networks than was previously possible with exhaustive enumeration algorithms.
Posted Content
Listing All Maximal Cliques in Sparse Graphs in Near-optimal Time
TL;DR: There exists a nearly-optimal fixed-parameter tractable algorithm for enumerating all maximal cliques, parametrized by degeneracy, and this algorithm matches the Θ(d(n − d)3 d/3) worst-case output size of the problem whenever n − d = Ω(n).
Book ChapterDOI
Listing All Maximal Cliques in Sparse Graphs in Near-optimal Time
TL;DR: In this article, a nearly optimal fixed-parameter tractable algorithm for enumerating all maximal cliques, parametrized by degeneracy, was presented, which runs in time O(dn3 d/3).
Journal ArticleDOI
A note on the problem of reporting maximal cliques
F. Cazals,C. Karande +1 more
TL;DR: This note shows that the strategy of Tomita et al. is a simple modification of the Bron-Kerbosch algorithm, based on an (un-exploited) observation raised in Koch's paper.
References
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Journal ArticleDOI
Corrections to Bierstone's Algorithm for Generating Cliques
TL;DR: The counterexamples to their and the modified version of the Bierstone algorithm for finding the set of cliques of a finite undirected linear graph are presented.