Hypernetworks: Multidimensional relationships in multilevel systems

摘要

Networks provide a powerful way of modelling the dynamicsudof complex systems. Going beyond binary relations, embracing -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 -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.