1. Functional Complexity Based on Topology

  1. Matthias Dehmer2,
  2. Abbe Mowshowitz3 and
  3. Frank Emmert-Streib3
  1. Hildegard Meyer-Ortmanns

Published Online: 12 JUL 2013

DOI: 10.1002/9783527670468.ch01

Advances in Network Complexity

Advances in Network Complexity

How to Cite

Meyer-Ortmanns, H. (2013) Functional Complexity Based on Topology, in Advances in Network Complexity (eds M. Dehmer, A. Mowshowitz and F. Emmert-Streib), Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany. doi: 10.1002/9783527670468.ch01

Editor Information

  1. 2

    UMIT, Institut für Bioinformatik und, Translationale Forschung, Eduard-Wallnöfer-Zentrum 1, 6060 Hall in Tyrol, Austria

  2. 3

    The City College of New York, Department of Computer Science, 138th Street at Convent Avenue, New York, NY 10031, USA

Author Information

  1. Jacobs University Bremen, School of Engineering and Science, Campus Ring 8, 28759, Bremen, Germany

Publication History

  1. Published Online: 12 JUL 2013
  2. Published Print: 10 JUL 2013

ISBN Information

Print ISBN: 9783527332915

Online ISBN: 9783527670468



  • topological complexity;
  • Jones polynomials;
  • Hopf link;
  • Kauffman bracket;
  • Boolean functions;
  • Boolean networks;
  • genetic networks;
  • transport networks


We describe a complexity measure that is supposed to be sensitive to the functional complexity of a network, when the network represents a dynamical system. The measure is formulated in terms of so-called admissible resolution patterns of the graph associated with the network, and its value depends on the specific dynamical constraints. We give examples for possible applications to networks of information, transport, regulation and computation. Relations of the complexity measure to link invariants, in particular to Kauffman brackets for Jones polynomials are indicated.