title: Emergent complex network geometry.
abstract: Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant for routing problems, inference and data mining. In real growing networks, topological, structural and geometrical properties emerge spontaneously from their dynamical rules. Nevertheless we still miss a model in which networks develop an emergent complex geometry. Here we show that a single two parameter network model, the growing geometrical network, can generate complex network geometries with non-trivial distribution of curvatures, combining exponential growth and small-world properties with finite spectral dimensionality. In one limit, the non-equilibrium dynamical rules of these networks can generate scale-free networks with clustering and communities, in another limit planar random geometries with non-trivial modularity. Finally we find that these properties of the geometrical growing networks are present in a large set of real networks describing biological, social and technological systems.
authors.affiliation: Beijing Key Lab of Traffic Data Analysis and Mining, School of Computer and Information Technology, Beijing Jiaotong University, Beijing 100044, China.
authors.forename: Zhihao
authors.initials: Z
authors.lastname: Wu
authors.affiliation: Department of Physics and Astronomy and INFN Sez. Bologna, Bologna University, Viale B. Pichat 6/2 40127 Bologna, Italy.
authors.forename: Giulia
authors.initials: G
authors.lastname: Menichetti
authors.affiliation: Karlsruhe Institute of Technology, Institute for Theoretical Physics, 76128 Karlsruhe, Germany.
authors.forename: Christoph
authors.initials: C
authors.lastname: Rahmede
authors.affiliation: School of Mathematical Sciences, Queen Mary University of London, E1 4NS London, United Kingdom.
authors.forename: Ginestra
authors.initials: G
authors.lastname: Bianconi
mesh_terms: D000465:Algorithms; D008962:Models, Theoretical