Hypernetworks: Multidimensional relationships in multilevel systems
The Open University, Milton Keynes, MK17 6AA, UK
Received: 28 March 2016
Revised: 26 July 2016
Published online: 30 September 2016
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.
© The Author(s) 2016
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