Network geometry

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 latent spaces underlying many networks, and effective dynamical processes networks. These three approaches to all intimately related, them have been found be exceptionally efficient discovering fractality, scale-invariance, self-similarity, other fundamental symmetries Network also great utility variety practical applications, ranging from understanding how brain works, routing Internet. Here, we review most important theoretical developments dealing with these last two decades, offer perspectives on future research directions challenges this novel frontier study complexity.