A difference equation approach to statistical mechanics of complex networks

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 F-distribution. 作者： Author： Jin-li GUO 作者單位： Business School, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China 期 刊： 應(yīng)用數(shù)學(xué)和力學(xué)（英文版）   EISCI Journal： APPLIED MATHEMATICS AND MECHANICS 年，卷(期)： 2009, 30(8) 分類號(hào)： N94 Keywords： complex network    degree distribution    scale-free network    機(jī)標(biāo)分類號(hào)： O4 TP2 機(jī)標(biāo)關(guān)鍵詞： complex networks    statistical mechanics    approach    degree distributions    difference equation    Poisson process    existence    problems    theory    paper    based    avoid 基金項(xiàng)目： 國家自然科學(xué)基金，the Foundation of Shanghai Leading Academic Discipline Project A difference equation approach to statistical mechanics of complex networks[期刊論文]  應(yīng)用數(shù)學(xué)和力學(xué)（英文版） --2009, 30(8)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 appr...

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