Complex network construction method on basis of matrix operation

Abstract

The invention discloses a complex network construction method on the basis of matrix operation. A complex network is constructed by Kronecker sum operation and Kronecker product operation on the basis of a plurality of generated network adjacent matrices. The complex network construction method comprises the main steps of: determining a generated network set; calculating a generated network adjacent matrix set; calculating a generated network degree distribution polynomial set; calculating an adjacent matrix of the complex network; calculating a degree distribution polynomial of the complex network; and the like. The complex network obtained by adopting the method is different from other classical networks, such as a random network, a small-world network, a scale-free network, a self-similar network and the like. Moreover, a degree distribution polynomial expressing method is adopted, operation of times multiplication and coefficient addition of common polynomial multiplication is adopted for Kronecker sum operation and operation of times multiplication and coefficient addition of similar polynomial multiplication is adopted for Kronecker product operation, and thus, the degree distribution of the type of complex network can be theoretically and strictly calculated. Particularly, the random network can be obtained by Kronecker sum operation on the basis of a plurality of generated network adjacent matrices.

Description

technical field [0001] The invention belongs to the field of electrical digital data processing, and is particularly suitable for a data processing method with specific functions, and in particular relates to a complex network construction method based on a plurality of Kronecker sum operations and Kronecker product operations for generating network adjacency matrices. 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 introduction of the ER random network model initiated the systematic research on complex networks and led the subsequent research on ...

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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 on random networks, small-world networks, scale-free networks and self-similar networks, etc. and methods, 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 required

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