Networks are finite metric spaces, with distances defined by the shortest paths between nodes. However, this is not the only form of network geometry: two others 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 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 use in a variety of practical applications, from understanding how the brain works to routing in the Internet. We review the most important theoretical and practical developments dealing with these approaches to network geometry and offer perspectives on future research directions and challenges in this frontier in the study of complexity.

网络是有限的度量空间，其距离由节点之间的最短路径定义。但是，这不是网络几何的唯一形式：另外两个是许多网络下面的潜在空间的几何，以及网络中动态过程引起的有效几何。这三种网络几何方法密切相关，并且发现这三种方法在发现网络的分形性，尺度不变性，自相似性和其他形式的基本对称性方面异常有效。从了解大脑的工作原理到Internet进行路由，网络几何在各种实际应用中也很有用。