25
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      From time series to complex networks: the visibility graph

      Preprint
      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          In this work we present a simple and fast computational method, the visibility algorithm, that converts a time series into a graph. The constructed graph inherits several properties of the series in its structure. Thereby, periodic series convert into regular graphs, and random series do so into random graphs. Moreover, fractal series convert into scale-free networks, enhancing the fact that power law degree distributions are related to fractality, something highly discussed recently. Some remarkable examples and analytical tools are outlined in order to test the method's reliability. Many different measures, recently developed in the complex network theory, could by means of this new approach characterize time series from a new point of view.

          Related collections

          Most cited references13

          • Record: found
          • Abstract: found
          • Article: found
          Is Open Access

          Emergence of scaling in random networks

          Systems as diverse as genetic networks or the world wide web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This feature is found to be a consequence of the two generic mechanisms that networks expand continuously by the addition of new vertices, and new vertices attach preferentially to already well connected sites. A model based on these two ingredients reproduces the observed stationary scale-free distributions, indicating that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.
            Bookmark
            • Record: found
            • Abstract: found
            • Article: found
            Is Open Access

            The structure and function of complex networks

            M. Newman (2003)
            Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.
              Bookmark
              • Record: found
              • Abstract: found
              • Article: found
              Is Open Access

              Statistical mechanics of complex networks

              Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.
                Bookmark

                Author and article information

                Journal
                06 October 2008
                Article
                10.1073/pnas.0709247105
                18362361
                0810.0920
                cc9233e4-730d-48ee-a294-39841c159bbb

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                PNAS, vol. 105, no. 13 (2008) 4972-4975
                physics.data-an

                Comments

                Comment on this article