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2016 ; 6
(ä): 36648
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Non-uniform Evolving Hypergraphs and Weighted Evolving Hypergraphs
#MMPMID27845334
Guo JL
; Zhu XY
; Suo Q
; Forrest J
Sci Rep
2016[Nov]; 6
(ä): 36648
PMID27845334
show ga
Firstly, this paper proposes a non-uniform evolving hypergraph model with
nonlinear preferential attachment and an attractiveness. This model allows nodes
to arrive in batches according to a Poisson process and to form hyperedges with
existing batches of nodes. Both the number of arriving nodes and that of chosen
existing nodes are random variables so that the size of each hyperedge is
non-uniform. This paper establishes the characteristic equation of hyperdegrees,
calculates changes in the hyperdegree of each node, and obtains the stationary
average hyperdegree distribution of the model by employing the Poisson process
theory and the characteristic equation. Secondly, this paper constructs a model
for weighted evolving hypergraphs that couples the establishment of new
hyperedges, nodes and the dynamical evolution of the weights. Furthermore, what
is obtained are respectively the stationary average hyperdegree and hyperstrength
distributions by using the hyperdegree distribution of the established unweighted
model above so that the weighted evolving hypergraph exhibits a scale-free
behavior for both hyperdegree and hyperstrength distributions.