Hypernetworks: Multidimensional relationships in multilevel systems

Johnson, J.H. (2016). Hypernetworks: Multidimensional relationships in multilevel systems. European Physical Journal Special Topics, 225(6) pp. 1037–1052.

DOI: https://doi.org/10.1140/epjst/e2016-02653-4

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.

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