Open AccessEmergence of scaling in non-uniform hypernetworksdoes the rich get richer lead to a power-law distribution?
Author(s) -
Jun Guo
Publication year - 2014
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.63.208901
Subject(s) - distribution (mathematics) , statistical physics , computer science , power law , poisson distribution , nonlinear system , scaling , process (computing) , exponential function , exponential distribution , topology (electrical circuits) , mathematics , physics , mathematical analysis , geometry , statistics , quantum mechanics , combinatorics , operating system
In this paper, we propose a hypernetwork model with a nonlinear preferential attachment, and study the evolving mechanism and topological properties of the hypernetwork. We analyze the model by using a Poisson process theory and a continuous technique, and give a characteristic equation of hyperdegrees. We obtain the stationary average hyperdegree distribution of the hypernetwork by the characteristic equation. The analytical result shows that the hypernetwork has a phenomenon of the rich get richer, and it accords well with the simulation. It is shown in this paper that the hyperdegree distribution of the dynamic model exhibits a stretched exponential distribution with the increase of the hypernetwork size. It proves that the rich get richer does not necessarily induce a power-law distribution.