From networks to hypernetworks in complex systems science

From networks to hypernetworks in complex systems science

Jeffrey Johnson

(Open University, UK)



Complex systems have multilevel dynamics emerging from interactions between their parts. Networks have provided deep insights into those dynamics, but only represent relations between two things while the generality is relations between many things. Hypergraphs and their related Galois connections have long been used to model such relations, but their set theoretic nature has inadequate and inappropriate structure. Simplicial complexes can better represent relations between many things but they too have limitations. Hypersimplices, which are defined as simplices in which the relational structure is explicit, overcome these limitations. Hypernetworks, which in the simplest cases are sets of hypersimplices, have a multidimensional connectivity structure which constrains those dynamics represented by patterns of numbers over the hypersimplices and their vertices. The dynamics of hypernetwork also involve the formation and disintegration of hypersimplices, which are seen as structural events related to system time. Hypernetworks provide algebraic structure able to represent multilevel systems and combine their top-down and bottom-up micro, meso and macro-dynamics. Hypernetworks naturally generalise graphs, hypergraphs and networks. These ideas will be presented in a graphical way through examples which also show the relevance of hypernetworks to policy. It will be argued that hypernetworks are necessary if not sufficient for a science of complex systems and its applications. The talk will be aimed at a general audience and no prior knowledge will be assumed.



Jeffrey Johnson

Centre for Complexity and Design

The Open University, Milton Keynes, MK7 6AA, UK

00 44 1908 652627, 00 44 77 966 966 21



Jeffrey Johnson is Professor of Complexity and Design at the Open University in the UK. Before this he was a researcher in the Geography Department at Cambridge University and in the Mathematics Department of Essex University. His PhD is in mathematics and his research involves creating a mathematical formalism able to unify the micro, meso and macro-dynamics of multilevel complex systems. He has developed this theory through many academic and commercial applications. He is very interested in the design of complex systems in a policy context. He is a past president of the Complex Systems Society, is currently a member of its Executive Committee, and is a Council member of the UNESCO UniTwin Complex Systems Digital Campus. He is CEO of Vision Scientific Ltd, a company he founded twenty five years ago. He has written extensively on complex systems and his latest book, Hypernetworks in the science of complex systems, was recently published by Imperial College Press.






Johnson, J. H., Hypernetworks in the science of complex systems, Imperial College Press (London), 2014.

Johnson, Jeffrey (2012). ‘Hypernetworks for policy design in systems of systems of systems’. In: 2nd International Conference on Complex Sciences: Theory and Applications, 5-7 Dec 2012, Santa Fe, Springer- Verlag, pp. 179–189.

Challenges in complex systems science’, San Miguel, M.; Johnson, J. H.; Kertesz, J.; Kaski, K.; Diaz-Guilera, A.; MacKay, R. S.; Loreto, V.; Erdi, P. and Helbing, D. (2012). Challenges in complex systems science. European Physics Journal Special Topics, 214 pp. 245–271.

Johnson, Jeffrey (2012). ‘Cities: systems of systems of systems’. In: Portugali, Juval; Meyer, Han; Stolk, Egbert and Tan, Ekim eds. Complexity Theories of Cities Have Come of Age. Springer Complexity. Berlin: Springer-Verlag, pp. 153–172.