Complex network construction method based on matrix product

A complex network and construction method technology, applied in the field of electrical digital data processing, can solve problems that cannot fully reflect various characteristics

Inactive Publication Date: 2014-11-05
SOUTHWEST JIAOTONG UNIV
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Problems solved by technology

[0011] Generally speaking, the research on the characteristics of complex networks is still a hot spot in complex network research today. It is undeniable that although there are relatively mature theories and methods for random networks, small-world networks, scale-free networks and self-similar networks method, most of the studies are also consistent with real complex networks, but still cannot fully reflect the various characteristics of real complex networks in real life, and further research on the characteristics of complex networks is needed

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  • Complex network construction method based on matrix product
  • Complex network construction method based on matrix product
  • Complex network construction method based on matrix product

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Embodiment Construction

[0051] A complex network construction method based on matrix product, comprising the following steps:

[0052] (1) Determine the generated network set U G ={G 1 , G 2 , G 3 ,...,G i ,...};

[0053] (2) Calculate and generate network set U G All networks in G i The adjacency matrix A(G i ), to get the generated network set U G The adjacency matrix set U A(G) ={A(G 1 ), A(G 2 ), A(G 3 ),…, A(G i ),...}:

[0054]In generating the network set U G , for any generator network G with n nodes, its adjacency matrix A(G) is an n×n square matrix, where for each data in the square matrix, if node i is adjacent to node j, then there is A(G)(i,j)=1, otherwise, A(G)(i,j)=0; if the number of links in the generated network G is m, the number of 1s in the adjacency matrix A(G) is also is m, and the network density of the generated network Density = 2 m n ( ...

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Abstract

The invention discloses a new complex network construction method based on a matrix product. The new complex network construction method based on the matrix product comprises the following main steps: determining a generation network set, calculating a generation network adjacency matrix set, determining a generation network degree distribution polynomial set, calculating a complex network adjacency matrix, and calculating the degree distribution of the complex network. On the basis of the Kronecker product of a plurality of generation network adjacency matrixes, the complex network is constructed, different generation networks and different amounts of generation networks are selected or the sequence of the Kronecker product of the generation network adjacency matrixes is regulated to obtain different generation networks. The complex network obtained by the invention is different from general random networks, small-world networks, scale-free networks and self-similar networks. In addition, through operations of the frequency multiplication and the coefficient multiplication of the degree distribution polynomial expression form of the complex network, the degree distribution of the type of complex network can be theoretically calculated strictly.

Description

technical field [0001] The invention belongs to the field of electric digital data processing, and is particularly suitable for a data processing method with specific functions, and in particular relates to a supernetwork construction method based on a simple Tracy-Singh product operation for generating a supernetwork adjacency matrix. Background technique [0002] The deepening of complex network research has promoted the rise of network science, and the research objects in many fields such as natural science and social science can be abstracted into complex networks for research. The construction of complex network models occupies an extremely important position in the analysis and research of social networks, computer networks, virtual social networks and other fields. In the middle of the last century, the ER stochastic network model was proposed to initiate systematic research on complex networks; at the end of the last century, the WS small-world network model and BA s...

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F19/00
Inventor 李天瑞刘胜久珠杰王红军
Owner SOUTHWEST JIAOTONG UNIV
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