Jeff Johnson -- Abstract

Hypernetworks and multilevel dynamics in complex systems

Graphs and networks have proved a powerful means of analysing binary relations between pairs of things. This talk will show how they can be extended naturally to the general case of n-ary relations between n things. Hypergraphs provide a set-theoretic generalisation of graphs but they are not rich enough. What I will call the 'hypernetwork', provides a much more powerful means of modelling relations and relations between relations. Based on simplicial complexes, hyperworks have a multidimensional generalisation of the connectivity of graphs and networks. Like hypergraphs they have a Galois lattice connectivity structure, and this is fundamental to the dynamics of systems. It will be shown that n-ary relations lead naturally to multilevel structure, and hypernetworks form a natural backcloth for the dynamic traffic of intra-level and inter-level system activity. Furthermore, hypernetworks have their own dynamics leading to a discrete view of system time. It will be argued that these structures are necessary if not sufficient for understanding the multilevel dynamics of complex systems. The talk will be developed through examples.

Page modified Mar 2006 by Richard G. Clegg