2020/01/31 by Marian Boguna, Marián Boguñá, Ivan Bonamassa +5 · 2 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · Mathematics · Physics and Astronomy · #Artificial intelligence #Combinatorics #Complex Network Analysis Techniques #Complex geometry #Complex network #Computer network #Computer science #Convex geometry #Discrete geometry #Engineering #Gene Regulatory Network Analysis #Geometry #Geometry and topology #Homogeneous space #Mathematics #Metric (unit) #Path (computing) #Regular polygon #Topological and Geometric Data Analysis #Topology (electrical circuits) #Variety (cybernetics) #cond-mat.dis-nn #cs.SI #physics.soc-ph
paper · pdf · doi:10.1038/s42254-020-00264-4
published as Nature Reviews Physics, v.3, 114-135, 2021
openalex created_date 2020/01/23 · arxiv created 2020/10/28 · openalex publication_date 2021/01/29 · arxiv updated 2021/02/16 · openalex updated_date 2026/08/05
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.