Hypernetworks: Multidimensional relationships in multilevel systems

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 o...

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Bibliographic Details
Published in:The European physical journal. ST, Special topics Special topics, 2016-09, Vol.225 (6-7), p.1037-1052
Main Author: Johnson, J.H.
Format: Article
Language:English
Subjects:
Atomic
Classical and Continuum Physics
Complex systems
Condensed Matter Physics
Graph theory
Graphs
Materials Science
Mathematical Modeling of Complex Systems
Measurement Science and Instrumentation
Molecular
Multilevel
Optical and Plasma Physics
Physics
Physics and Astronomy
Regular Article
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Summary: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.
ISSN:1951-6355
1951-6401
DOI:10.1140/epjst/e2016-02653-4