title: Locating the source of diffusion in complex networks by time-reversal backward spreading.
abstract: Locating the source that triggers a dynamical process is a fundamental but challenging problem in complex networks, ranging from epidemic spreading in society and on the Internet to cancer metastasis in the human body. An accurate localization of the source is inherently limited by our ability to simultaneously access the information of all nodes in a large-scale complex network. This thus raises two critical questions: how do we locate the source from incomplete information and can we achieve full localization of sources at any possible location from a given set of observable nodes. Here we develop a time-reversal backward spreading algorithm to locate the source of a diffusion-like process efficiently and propose a general locatability condition. We test the algorithm by employing epidemic spreading and consensus dynamics as typical dynamical processes and apply it to the H1N1 pandemic in China. We find that the sources can be precisely located in arbitrary networks insofar as the locatability condition is assured. Our tools greatly improve our ability to locate the source of diffusion in complex networks based on limited accessibility of nodal information. Moreover, they have implications for controlling a variety of dynamical processes taking place on complex networks, such as inhibiting epidemics, slowing the spread of rumors, pollution control, and environmental protection.
authors.affiliation: School of Systems Science, Beijing Normal University, Beijing, 100875, P. R. China.
authors.forename: Zhesi
authors.initials: Z
authors.lastname: Shen
authors.affiliation: School of Finance, University of International Business and Economics, Beijing, 100029, P. R. China.
authors.forename: Shinan
authors.initials: S
authors.lastname: Cao
authors.affiliation: School of Systems Science, Beijing Normal University, Beijing, 100875, P. R. China.|Business School, University of Shanghai for Science and Technology, Shanghai 200093, China.
authors.forename: Wen-Xu
authors.initials: WX
authors.lastname: Wang
authors.affiliation: School of Systems Science, Beijing Normal University, Beijing, 100875, P. R. China.
authors.forename: Zengru
authors.initials: Z
authors.lastname: Di
authors.affiliation: Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
authors.forename: H Eugene
authors.initials: HE
authors.lastname: Stanley
mesh_terms: D004058:Diffusion; D006801:Humans; D053118:Influenza A Virus, H1N1 Subtype / Q000502:physiology; D007251:Influenza, Human / Q000453:epidemiology / Q000635:transmission; D008962:Models, Theoretical; D058873:Pandemics; D013997:Time Factors