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.
10th ECCO / GBI seminar series. Spring 2014
From networks to hypernetworks in complex systems science
April 18, 2014, Brussels
Jeffrey Johnson Open University, UK
Slides, references and more: http://ecco.vub.ac.be/?q=node/231
Via Complexity Digest