Weber Sebastian, Porto Markus
Institut für Festkörperphysik, Technische Universität Darmstadt, Hochschulstrasse 8, 64289 Darmstadt, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Oct;76(4 Pt 2):046111. doi: 10.1103/PhysRevE.76.046111. Epub 2007 Oct 18.
Random networks are intensively used as null models to investigate properties of complex networks. We describe an efficient and accurate algorithm to generate arbitrarily two-point degree-degree correlated undirected random networks without self-edges or multiple edges among vertices. With the goal to systematically investigate the influence of two-point correlations, we furthermore develop a formalism to construct a joint degree distribution P(j,k) , which allows one to fix an arbitrary degree distribution P(k) and an arbitrary average nearest neighbor function k_{nn}(k) simultaneously. Using the presented algorithm, this formalism is demonstrated with scale-free networks [P(k) proportional, variantk;{-gamma}] and empirical complex networks [ P(k) taken from network] as examples. Finally, we generalize our algorithm to annealed networks which allows networks to be represented in a mean-field-like manner.
随机网络被广泛用作空模型来研究复杂网络的性质。我们描述了一种高效且准确的算法，用于生成无自环且顶点间无多重边的任意两点度-度相关的无向随机网络。为了系统地研究两点相关性的影响，我们进一步开发了一种形式体系来构建联合度分布(P(j,k))，它允许同时固定任意度分布(P(k))和任意平均最近邻函数(k_{nn}(k))。使用所提出的算法，以无标度网络([P(k))正比于(k^{-\gamma}])和经验复杂网络([P(k))取自网络()])为例展示了这种形式体系。最后，我们将算法推广到退火网络，这使得网络能够以类似平均场的方式表示。
