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      Colloquium : Criticality and dynamical scaling in living systems

      Reviews of Modern Physics
      American Physical Society (APS)

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          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.
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            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.
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              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.
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                Author and article information

                Journal
                RMPHAT
                Reviews of Modern Physics
                Rev. Mod. Phys.
                American Physical Society (APS)
                0034-6861
                1539-0756
                July 2018
                July 10 2018
                : 90
                : 3
                Article
                10.1103/RevModPhys.90.031001
                9c38eede-1a11-40e4-92c2-7858ff7e2c06
                © 2018

                https://link.aps.org/licenses/aps-default-license


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