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Embracing n-ary Relations in Network Science

Johnson, Jeffrey H. (2016). Embracing n-ary Relations in Network Science. In: Wierzbicki, Adam; Brandes, Ulrik; Schweitzer, Frank and Pedreschi, Dino eds. Advances in Network Science: 12th International Conference and School, NetSci-X 2016, Wroclaw, Poland, January 11-13, 2016, Proceedings. Lecture Notes in Computer Science (9564). Switzerland: Springer, pp. 147–160.

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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.

Item Type: Book Section
Copyright Holders: 2016 Springer International Publishing
ISBN: 3-319-28360-X, 978-3-319-28360-9
Keywords: n-ary relation; graph; hypergraph; network; simplicial complex; multiplex network; hypernetwork
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Engineering and Innovation
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Research Group: Centre for Policing Research and Learning (CPRL)
Design and Innovation
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Item ID: 44898
Depositing User: Jeffrey Johnson
Date Deposited: 22 Dec 2015 11:07
Last Modified: 05 Apr 2020 17:12
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