论文标题
复杂网络中的几何重归其化流量的有限尺寸缩放
Finite-size scaling of geometric renormalization flows in complex networks
论文作者
论文摘要
最近，几何重归其化组的概念为研究复杂网络的结构对称性和功能不变性提供了良好的方法。沿着这条线，我们系统地研究了合成和真实进化网络的几何重新归一化流中结构和动力学可观察力的有限尺寸缩放。我们的结果表明，这些可观察物可以通过一定的缩放函数来很好地表征。具体而言，我们表明，缩放函数所隐含的关键指数与这些可观察到的无关，但仅取决于网络的小世界属性，即，位于小世界中的所有网络都有一个均匀的缩放指数，而位于非微不足道的阶段的缩放量表指数均匀。更重要的是，我们对具有小世界特征的真实进化网络进行了广泛的实验，我们的结果表明，这些可观察到的物品在其几何重新归一化流程中也具有统一的缩放。因此，从某种意义上说，该指数可以用作分类通用小世界和非小世界网络模型的有效度量。
Recently, the concept of geometric renormalization group provides a good approach for studying the structural symmetry and functional invariance of complex networks. Along this line, we systematically investigate the finite-size scaling of structural and dynamical observables in geometric renormalization flows of synthetic and real evolutionary networks. Our results show that these observables can be well characterized by a certain scaling function. Specifically, we show that the critical exponent implied by the scaling function is independent of these observables but only depends on the small-world properties of the network, namely, all networks located in the small-world phase have a uniform scaling exponent, while those located in the non-small-world phase and in their critical regions have another uniform scaling. More importantly, we perform extensive experiments on real evolutionary networks with small-world characteristics, and our results show that these observables also have uniform scaling in their geometric renormalization flows. Therefore, in a sense this exponent can be used as an effective measure for classifying universal small-world and non-small-world network models.
