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Two characters, scale-free and hierarchical structure, are shown in lots of real systems all over the world. In this article, firstly, we build up a class of network models with hierarchical structure, denoted by Nh(t), and prove it to be scale-free. By computing average degrees, we find these network models are all sparse. Secondly, based on their special topological structure, we research analytically...
Many articles research network scale-free nature from the angle of the topology, this research from the angle of the dynamic equation of the scale-free of network. So far network operation, there is no exact definition, in this article we simply introduce several kinds of network operation. A class of network models, called the compound models, are constructed for understanding and comparing network...
For understanding dynamical phenomena Barabási and Albert shown a process that has been a useful mathematical method, and was changed in various forms and applied in researching of scale-free networks. We focus on dynamic differential equations like that by Barabási and Albert, and construct network models by the typical and generalized dynamic differential equations. Analysis of degree distribution...
In order to make it easier to study the scale-free nature of the complex network, and to explore the topological structures of networks by mathematical methods. There are many successful mathematical methods shown in scale-free networks that are forming branches of mathematics and network science. We are motivated from the cumulative degree distribution and edge cumulative degree distribution of scale-free...
Multiple-partite networks exist in the real world, such as engineering constructions consisted of workers and machines. We build up random multiple-partite network models and show their topological properties by means of well-known methods appeared in the Barabási-Albert model. We find some new characters of the Barabási-Albert model and BA-type models, and show a connection between the degree distribution...
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