Abstract
To depict the complex relationship among nodes and the evolving process of a complex system, a Bose-Einstein hypernetwork is proposed in this paper. Based on two basic evolutionary mechanisms, growth and preference jumping, the distribution of hyperedge cardinalities is studied. The Poisson process theory is used to describe the arrival process of new node batches. And, by using the Poisson process theory and a continuity technique, the hypernetwork is analyzed and the characteristic equation of hyperedge cardinalities is obtained. Additionally, an analytical expression for the stationary average hyperedge cardinality distribution is derived by employing the characteristic equation, from which Bose-Einstein condensation in the hypernetwork is obtained. The theoretical analyses in this paper agree with the conducted numerical simulations. This is the first study on the hyperedge cardinality in hypernetworks, where Bose-Einstein condensation can be regarded as a special case of hypernetworks. Moreover, a condensation degree is also discussed with which Bose-Einstein condensation can be classified.
Highlights
As an effective tool to characterize complex systems, the studies of complex networks have attracted much attention in the past decade
Komarov and Pikovsky reported on finite-sized-induced transitions to synchrony in a population of phase oscillators coupled via nonlinear mean field, which is microscopically equivalent to a hypernetwork organization of interactions[9]
The content of Wikipedia was described with a hypernetwork model[10], it represents just a special case of the general evolution model of complex networks in ref
Summary
Condensation in Hypernetworks received: 16 April 2016 accepted: 30 August 2016 Published: 27 September 2016. The theoretical analyses in this paper agree with the conducted numerical simulations This is the first study on the hyperedge cardinality in hypernetworks, where Bose-Einstein condensation can be regarded as a special case of hypernetworks. Wang et al.[13] offered a hypernetwork dynamic evolution model with growth and preferential attachment mechanisms, where at each time step some new nodes are added and connected to an old node through a hyperedge. The structural properties, including the degree distribution in different layers and different types of correlations have been obtained Contrary to these works, the originality of our present work is to regard particles as nodes and energy levels as hyperedges, on which an evolving hypernetwork model is developed and its essential properties are studied. Our presentation is concluded with some conclusion remarks
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