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Embracing n-ary Relations in Network Science

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Advances in Network Science (NetSci-X 2016)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9564))

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Abstract

Most network scientists restrict their attention to relations between pairs of things, even though most complex systems have structures and dynamics determined by n-ary relation where n is greater than two. Various examples are given to illustrate this. The basic mathematical structures allowing more than two vertices have existed for more than half a century, including hypergraphs and simplicial complexes. To these can be added hypernetworks which, like multiplex networks, allow many relations to be defined on the vertices. Furthermore, hypersimplices provide an essential formalism for representing multilevel part-whole and taxonomic structures for integrating the dynamics of systems between levels. Graphs, hypergraphs, networks, simplicial complex, multiplex network and hypernetworks form a coherent whole from which, for any particular application, the scientist can select the most suitable.

Supported by the European Dynamics of Multi-Level Complex Systems (DyM-CS) FP7 FET programme, http://cordis.europa.eu/fp7/ict/fet-proactive/dymcs_en.html.

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Author information

Authors and Affiliations

  1. Topdrim Project, The Open University, Milton Keynes, MK7 6AA, UK

    Jeffrey H. Johnson

Authors
  1. Jeffrey H. Johnson
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Correspondence to Jeffrey H. Johnson .

Editor information

Editors and Affiliations

  1. Polish-Japanese Academy, Warzaw, Poland

    Adam Wierzbicki

  2. Universität Konstanz, Konstanz, Baden-Württemberg, Germany

    Ulrik Brandes

  3. ETH Zürich, Zürich, Switzerland

    Frank Schweitzer

  4. University of Pisa, Pisa, Italy

    Dino Pedreschi

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Johnson, J.H. (2016). Embracing n-ary Relations in Network Science. In: Wierzbicki, A., Brandes, U., Schweitzer, F., Pedreschi, D. (eds) Advances in Network Science. NetSci-X 2016. Lecture Notes in Computer Science(), vol 9564. Springer, Cham. https://doi.org/10.1007/978-3-319-28361-6_12

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  • DOI: https://doi.org/10.1007/978-3-319-28361-6_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-28360-9

  • Online ISBN: 978-3-319-28361-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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