title: Correlation dimension of complex networks.
abstract: We propose a new measure to characterize the dimension of complex networks based on the ergodic theory of dynamical systems. This measure is derived from the correlation sum of a trajectory generated by a random walker navigating the network, and extends the classical Grassberger-Procaccia algorithm to the context of complex networks. The method is validated with reliable results for both synthetic networks and real-world networks such as the world air-transportation network or urban networks, and provides a computationally fast way for estimating the dimensionality of networks which only relies on the local information provided by the walkers.
authors.affiliation: Departamento de Matemática Aplicada y Estadística, ETSI Aeronáuticos, Universidad Politécnica de Madrid, 28040 Madrid, Spain. lucas.lacasa@upm.es
authors.forename: Lucas
authors.initials: L
authors.lastname: Lacasa
authors.forename: Jesús
authors.initials: J
authors.lastname: Gómez-Gardeñes
mesh_terms: D000465:Algorithms; D019058:Community Networks; D008962:Models, Theoretical; D013269:Stochastic Processes; D014506:Urban Renewal