Listing All Maximal Cliques in Large Sparse Real-World Graphs

  • David Eppstein
  • Darren Strash
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6630)


We implement a new algorithm for listing all maximal cliques in sparse graphs due to Eppstein, Löffler, and Strash (ISAAC 2010) and analyze its performance on a large corpus of real-world graphs. Our analysis shows that this algorithm is the first to offer a practical solution to listing all maximal cliques in large sparse graphs. All other theoretically-fast algorithms for sparse graphs have been shown to be significantly slower than the algorithm of Tomita et al. (Theoretical Computer Science, 2006) in practice. However, the algorithm of Tomita et al. uses an adjacency matrix, which requires too much space for large sparse graphs. Our new algorithm opens the door for fast analysis of large sparse graphs whose adjacency matrix will not fit into working memory.


maximal clique listing Bron–Kerbosch algorithm sparse graphs d-degenerate graphs 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • David Eppstein
    • 1
  • Darren Strash
    • 1
  1. 1.Department of Computer ScienceUniversity of CaliforniaIrvineUSA

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