title: The geometric nature of weights in real complex networks.
abstract: The topology of many real complex networks has been conjectured to be embedded in hidden metric spaces, where distances between nodes encode their likelihood of being connected. Besides of providing a natural geometrical interpretation of their complex topologies, this hypothesis yields the recipe for sustainable Internet's routing protocols, sheds light on the hierarchical organization of biochemical pathways in cells, and allows for a rich characterization of the evolution of international trade. Here we present empirical evidence that this geometric interpretation also applies to the weighted organization of real complex networks. We introduce a very general and versatile model and use it to quantify the level of coupling between their topology, their weights and an underlying metric space. Our model accurately reproduces both their topology and their weights, and our results suggest that the formation of connections and the assignment of their magnitude are ruled by different processes.
authors.affiliation: Departament de Física de la Matèria Condensada, Universitat de Barcelona, Martí i Franquès 1, E-08028 Barcelona, Spain.|Universitat de Barcelona Institute of Complex Systems (UBICS), Barcelona, Spain.
authors.forename: Antoine
authors.initials: A
authors.lastname: Allard
authors.affiliation: Departament de Física de la Matèria Condensada, Universitat de Barcelona, Martí i Franquès 1, E-08028 Barcelona, Spain.|Universitat de Barcelona Institute of Complex Systems (UBICS), Barcelona, Spain.|Institució Catalana de Recerca i Estudis Avançats (ICREA), Passeig Lluís Companys 23, E-08010 Barcelona, Spain.
authors.forename: M Ángeles
authors.initials: MÁ
authors.lastname: Serrano
authors.affiliation: Departament de Física de la Matèria Condensada, Universitat de Barcelona, Martí i Franquès 1, E-08028 Barcelona, Spain.|Universitat de Barcelona Institute of Complex Systems (UBICS), Barcelona, Spain.
authors.forename: Guillermo
authors.initials: G
authors.lastname: García-Pérez
authors.affiliation: Departament de Física de la Matèria Condensada, Universitat de Barcelona, Martí i Franquès 1, E-08028 Barcelona, Spain.|Universitat de Barcelona Institute of Complex Systems (UBICS), Barcelona, Spain.
authors.forename: Marián
authors.initials: M
authors.lastname: Boguñá
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D008433:Mathematics; D008962:Models, Theoretical; D014894:Weights and Measures