Abstract
Networks provide a powerful way of modelling the dynamics of complex systems. Going beyond binary relations, embracing n-ary relations in network science can generalise many structures. This starts with hypergraphs and their Galois structures. Simplicial complexes generalise hypergraphs by adding orientation. Their multidimensional q-connectivity structure generalises connectivity in networks. Hypersimplices generalise simplices by making the relational structure explicit in the notation. This gives a new way of representing multilevel systems and their dynamics, leading to a new fragment-recombine operator to model the complex dynamics of interacting multilevel systems.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R.H. Atkin, I.J. Man-Machine Studies 4, 139 (1972)
R.H. Atkin Combinatorial connectivities in social systems, Birkhäuser (Basel) (1977)
C. Berge, ‘Sur certains hypergraphes généralisant les graphes bipartites’. In P. Erdös, A. Rhényi, V.T. Sós (eds), Combinatorial Theory and its Applications I, (Proc. Colloquium on Combinatorial Theory and its Applications, 119. North-Holland, 1970)
C. Berge, Hypergraphs: Combinatorics of Finite Sets (North Holland Amsterdam 1989)
S. Boccalettia, et al., Phys. Rep. 544, 1 (2014), https://arxiv.org/abs/1407.0742
N. Christakis, J. Fowler, Connected: The amazing power of social networks and how they shape our lives, (Harpur Press, London 2010)
R.I.M. Dunbar, J Hum. Evolu. 22, 469 (1992)
L.C. Freeman, D.R. White, 1993. ‘Using Galois lattices to represent network data’, Sociological methodology, Volume 23, American Sociological Association, ISBN 1-55786-464-0, ISSN 0081-1750, http://eclectic.ss.uci.edu/aaadrwhite/pw/Galois.pdf
J.H. Johnson, Hypernetworks in the science of complex systems, (Imperial College Press London 2014), http://www.hypernetworks.eu
Author information
Authors and Affiliations
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Johnson, J. Hypernetworks: Multidimensional relationships in multilevel systems. Eur. Phys. J. Spec. Top. 225, 1037–1052 (2016). https://doi.org/10.1140/epjst/e2016-02653-4
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjst/e2016-02653-4