## Recent Publications

### Hypernetworks in the Science of Complex Systems

*Jeffrey Johnson
*

### Embracing n-ary relations in network science

*Jeffrey Johnson*

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