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A difference equation approach to statistical mechanics of complex networks

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Abstract

In this paper, we propose a difference equation approach to the estimation of the degree distributions in growing networks after having analyzed the disadvantages of some existing approaches. This approach can avoid logic conflicts caused by the continuum of discrete problems, and does not need the existence assumption of the stationary degree distribution in the network analysis. Using this approach, we obtain a degree distribution formula of the Poisson growth and preferential attachment network. It is rigorously shown that this network is scale-free based on the Poisson process theory and properties of Γ-distribution.

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Authors and Affiliations

  1. Business School, University of Shanghai for Science and Technology, Shanghai, 200093, P. R. China

    Jin-li Guo  (郭进利)

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  1. Jin-li Guo  (郭进利)
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Correspondence to Jin-li Guo  (郭进利).

Additional information

Communicated by Li-qun CHEN

Project supported by the National Natural Science Foundation of China (No. 70871082) and the Foundation of Shanghai Leading Academic Discipline Project (No. S30504)

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Guo, Jl. A difference equation approach to statistical mechanics of complex networks. Appl. Math. Mech.-Engl. Ed. 30, 1063–1068 (2009). https://doi.org/10.1007/s10483-009-0813-6

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  • DOI: https://doi.org/10.1007/s10483-009-0813-6

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

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