Hypernetworks in the Science of Complex Systems
NetSciX 2016, Advances in Network Science, A. Wierzbicki, U. Brandes, F. Schweitzer, D. Pedreschi (Eds), Springer, 2016
Abstract: Most network scientists
restrict their attention to relations between pairs of things, even
though most complex systems have structures
and dynamics determined by n-ary relation where n is greater than two. Various examples are given to illustrate this. The basic mathematical structures allowing more than two vertices have existed for more than half a century, including hypergraphs and simplicial complexes. To these can be added hypernetworks which, like multiplex networks, allow many relations to be dened on the vertices. Furthermore, hypersimplices provide an essential formalism for representing multilevel partwhole and taxonomic structures for integrating the dynamics of systems between levels. Graphs, hypergraphs, networks, simplicial complex, multiplex network and hypernetworks form a coherent whole from which, for any particular application, the scientist can select the most suitable.
Keywords: n-ary relation, graph, hypergraph, network, simplicial complex, multiplex network, hypernetwork