更好地理解分形网络的特征
Towards a Better Understanding of the Characteristics of Fractal Networks
AI总结：
本文系统梳理并实证分析网络特征与分形性的关系，基于五个模型和六类真实网络区分分形网络的普遍属性与偶然假象。
摘要：
在过去二十年中，复杂网络的分形性质引起了广泛的研究兴趣。与几何分形类似，网络的分形性也可以通过所谓的盒覆盖法来定义。如果覆盖整个网络所需的最小盒子数量与盒子尺寸之间满足幂律关系，则该网络被称为分形网络。多年来，网络的分形性已与多种网络性质联系起来，例如异配性、枢纽节点之间的排斥、长程排斥相关性以及较低的边介数中心性。然而，这些论断通常基于定制的网络模型和少量真实网络，因此其普遍性常常受到质疑。由于分形网络已被证明具有重要性质，例如对蓄意攻击的鲁棒性，因此迫切需要揭示导致分形性的底层机制。因此，本工作的主要目标是更好地理解复杂网络中分形性的起源。为此，我们系统回顾了以往关于各种网络特征与分形性关系的研究结果。此外，我们在五个网络模型以及来自六个领域的大量真实网络上对这些关系进行了全面分析。我们阐明了哪些特征普遍存在于分形网络中，而哪些特征只是人为假象或巧合。
英文摘要：
The fractal nature of complex networks has received a great deal of research interest in the last two decades. Similarly to geometric fractals, the fractality of networks can also be defined with the so-called box-covering method. A network is called fractal if the minimum number of boxes needed to cover the entire network follows a power-law relation with the size of the boxes. The fractality of networks has been associated with various network properties throughout the years, for example, disassortativity, repulsion between hubs, long-range-repulsive correlation, and small edge betweenness centralities. However, these assertions are usually based on tailor-made network models and on a small number of real networks, hence their ubiquity is often disputed. Since fractal networks have been shown to have important properties, such as robustness against intentional attacks, it is in dire need to uncover the underlying mechanisms causing fractality. Hence, the main goal of this work is to get a better understanding of the origins of fractality in complex networks. To this end, we systematically review the previous results on the relationship between various network characteristics and fractality. Moreover, we perform a comprehensive analysis of these relations on five network models and a large number of real-world networks originating from six domains. We clarify which characteristics are universally present in fractal networks and which features are just artifacts or coincidences.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
