Isolation concepts for clique enumeration: Comparison and computational experiments

  • Authors:
  • Falk Hüffner;Christian Komusiewicz;Hannes Moser;Rolf Niedermeier

  • Affiliations:
  • School of Computer Science, Tel Aviv University, 69978 Tel Aviv, Israel;Institut für Informatik, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 2, D-07743 Jena, Germany;Institut für Informatik, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 2, D-07743 Jena, Germany;Institut für Informatik, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 2, D-07743 Jena, Germany

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2009

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Abstract

We do computational studies concerning the enumeration of isolated cliques in graphs. Isolation, as recently introduced, measures the degree of connectedness of the cliques to the rest of the graph. Isolation helps both in getting faster algorithms for the enumeration of maximal general cliques and in filtering out cliques with special semantics. We compare three isolation concepts and their combination with two enumeration modi for maximal cliques (''isolated maximal'' vs ''maximal isolated''). All studied concepts exhibit the fixed-parameter tractability of the enumeration task with respect to the parameter ''degree of isolation''. We provide a first systematic experimental study of the corresponding enumeration algorithms, using synthetic graphs (in the G"n","m","p model), financial networks, and a music artist similarity network, proposing the enumeration of isolated cliques as a useful instrument in analyzing financial and social networks.