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Finite-size scaling of geometric renormalization flows in complex networks
Physical Review E ( IF 2.4 ) Pub Date : 2021-09-10 , DOI: 10.1103/physreve.104.034304
Dan Chen 1 , Housheng Su 1 , Xiaofan Wang 2 , Gui-Jun Pan 3 , Guanrong Chen 4
Affiliation  

Some characteristics of complex networks need to be derived from global knowledge of the network topologies, which challenges the practice for studying many large-scale real-world networks. Recently, the geometric renormalization technique has provided a good approximation framework to significantly reduce the size and complexity of a network while retaining its “slow” degrees of freedom. However, due to the finite-size effect of real networks, excessive renormalization iterations will eventually cause these important “slow” degrees of freedom to be filtered out. In this paper, we systematically investigate the finite-size scaling of structural and dynamical observables in geometric renormalization flows of both 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 depends only on the structural properties of the network. To a certain extent, the results of this paper are of great significance for predicting the observable quantities of large-scale real systems and further suggest that the potential scale invariance of many real-world networks is often masked by finite-size effects.

中文翻译:

复杂网络中几何重整化流的有限尺度缩放

复杂网络的一些特征需要从网络拓扑的全局知识中推导出来,这对研究许多大规模现实世界网络的实践提出了挑战。最近,几何重整化技术提供了一个很好的近似框架,可以显着降低网络的规模和复杂性,同时保持其“慢”自由度。然而,由于真实网络的有限尺寸效应,过多的重整化迭代最终会导致这些重要的“慢”自由度被过滤掉。在本文中,我们系统地研究了合成和真实进化网络的几何重整化流中结构和动态可观察量的有限尺寸缩放。我们的结果表明,这些可观察量可以通过某个缩放函数很好地表征。具体来说,我们表明缩放函数所隐含的临界指数与这些可观察量无关,而仅取决于网络的结构特性。在一定程度上,本文的结果对于预测大规模真实系统的可观察量具有重要意义,并进一步表明许多真实世界网络的潜在尺度不变性往往被有限尺寸效应所掩盖。
更新日期:2021-09-10
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