Miller Gerald A, Shi Yi Y, Qian Hong, Bomsztyk Karol
Department of Physics, University of Washington Seattle, Seattle, WA 98195, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 May;75(5 Pt 1):051910. doi: 10.1103/PhysRevE.75.051910. Epub 2007 May 16.
The properties of certain networks are determined by hidden variables that are not explicitly measured. The conditional probability (propagator) that a vertex with a given value of the hidden variable is connected to k other vertices determines all measurable properties. We study hidden variable models and find an averaging approximation that enables us to obtain a general analytical result for the propagator. Analytic results showing the validity of the approximation are obtained. We apply hidden variable models to protein-protein interaction networks (PINs) in which the hidden variable is the association free energy, determined by distributions that depend on biochemistry and evolution. We compute degree distributions as well as clustering coefficients of several PINs of different species; good agreement with measured data is obtained. For the human interactome two different parameter sets give the same degree distributions, but the computed clustering coefficients differ by a factor of about 2. This shows that degree distributions are not sufficient to determine the properties of PINs.
某些网络的属性由未明确测量的隐藏变量决定。具有给定隐藏变量值的顶点与其他k个顶点相连的条件概率（传播子）决定了所有可测量的属性。我们研究隐藏变量模型，并找到一种平均近似方法，使我们能够获得传播子的一般解析结果。得到了表明该近似有效性的解析结果。我们将隐藏变量模型应用于蛋白质-蛋白质相互作用网络（PINs），其中隐藏变量是结合自由能，由依赖于生物化学和进化的分布决定。我们计算了不同物种的几个PINs的度分布和聚类系数；与实测数据吻合良好。对于人类相互作用组，两个不同的参数集给出相同的度分布，但计算出的聚类系数相差约2倍。这表明度分布不足以确定PINs的属性。
