论文标题
网络几何形状
Network Geometry
论文作者
论文摘要
真实网络是有限的度量空间。然而，网络中最短路径距离引起的几何形状绝对不是其唯一的几何形状。网络几何形式的其他形式是许多网络基础潜在空间的几何形状，以及网络中动态过程引起的有效几何形状。这三种网络几何形状的方法都是密切相关的，并且发现这三种方法在发现网络中的分形，比例性变革，自相似性和其他形式的基本对称性方面非常有效。网络几何形状在各种实际应用中也具有很大的实用性，从了解大脑的工作方式到互联网中的路由。在这里，我们回顾了过去二十年来涉及这些网络几何方法的最重要的理论和实践发展，并在复杂性研究中对这一小说领域的未来研究方向和挑战提供了观点。
Real networks are finite metric spaces. Yet the geometry induced by shortest path distances in a network is definitely not its only geometry. Other forms of network geometry are the geometry of latent spaces underlying many networks, and the effective geometry induced by dynamical processes in networks. These three approaches to network geometry are all intimately related, and all three of them have been found to be exceptionally efficient in discovering fractality, scale-invariance, self-similarity, and other forms of fundamental symmetries in networks. Network geometry is also of great utility in a variety of practical applications, ranging from the understanding how the brain works, to routing in the Internet. Here, we review the most important theoretical and practical developments dealing with these approaches to network geometry in the last two decades, and offer perspectives on future research directions and challenges in this novel frontier in the study of complexity.
