An evolving hypernetwork model and its properties

Hu, Feng; Zhao, Haixing; Ma, Xinfang

doi:10.1360/132012-87

Cited by 42 publications

(27 citation statements)

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“…[12] The node degree of a hyperedge e i , denoted as d(e i ), is the number of nodes that e i contains. Definition 2.3 [12] The node hyperdegree of a node x j , denoted as d H (x j ), is the number of hyperedges which contain x j . Definition 2.…”

Section: A Hypergraphmentioning

confidence: 99%

“…Note that Definition 2.4 is different from that in [12] since d hd (e k ) in this paper refers to the number of hyperedges adjacent to e k including e k itself while d hd (e k ) in [12] is the number of hyperedges adjacent to e k without including e k .…”

Section: Definition 22mentioning

confidence: 99%

“…Furthermore, they coined the term complex hyper-networks to designate such systems where nodes are grouped together in multi-dyadic relationships represented by hyper-edges. Hu et al built a new evolving hypernetwork model and presented some basic topological properties, e.g., node degrees, node hyperdegrees, and hyperedge degrees [12]. Presently, hypernetworks have received much attention.…”

Section: Introductionmentioning

confidence: 99%

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A New Hypernetwork Model Based on Matrix Operation

Liu

2015

2015 10th International Conference on Intelligent Systems and Knowledge Engineering (ISKE)

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In this paper, we propose a new hypernetwork model based on Tracy-Singh Product on the correlation matrix of hypergraph. Node degree, node hyperdegree, and hyperedge degree and their corresponding polynomials are introduced to describe this hypernetwork model. It is shown that this kind of hypernetworks is fractal as its correlation matrix is a fractal matrix. The fractal parameter is then given. What's more, this kind of hypernetworks is also small-world for the diameter won't exceed twice the diameter of primitive hypergraph. By a novel product of node degree polynomial, node hyperdegree polynomial and hyperedge degree polynomial, node degree, node hyperdegree and hyperedge degree are obtained.

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Section: A Hypergraphmentioning

confidence: 99%

Section: Definition 22mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A New Hypernetwork Model Based on Matrix Operation

Liu

2015

2015 10th International Conference on Intelligent Systems and Knowledge Engineering (ISKE)

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“…proposed a dynamic evolving model according to uniform growth and preferential attachment mechanisms, in which a new batch of nodes together with one existing node formed one hyperedge, and gradually formed the final network. Hu et al 25. proposed another dynamic model.…”

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confidence: 99%

Non-uniform Evolving Hypergraphs and Weighted Evolving Hypergraphs

Guo

Zhu

Suo

et al. 2016

Sci Rep

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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.

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“…However, complex hypernetworks can well solve the above problems, in which a hyperedge can contain more than two nodes. Thus, it is useful to represent the collaboration network as a hypernetwork in which nodes represent authors and hyperedges represent papers that have been coauthored by the groups of authors [16][17][18][19]. For example, we want to describe the fact that author '1' co-published a paper with author '2' and '3', co-published a paper with author '3' and '4', and co-published a paper with author '2', '3' and '4'.…”

mentioning

confidence: 99%