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      Universal resilience patterns in complex networks.

      1 , 2 , 1 , 3 , 4 , 5
      Nature

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          Abstract

          Resilience, a system's ability to adjust its activity to retain its basic functionality when errors, failures and environmental changes occur, is a defining property of many complex systems. Despite widespread consequences for human health, the economy and the environment, events leading to loss of resilience--from cascading failures in technological systems to mass extinctions in ecological networks--are rarely predictable and are often irreversible. These limitations are rooted in a theoretical gap: the current analytical framework of resilience is designed to treat low-dimensional models with a few interacting components, and is unsuitable for multi-dimensional systems consisting of a large number of components that interact through a complex network. Here we bridge this theoretical gap by developing a set of analytical tools with which to identify the natural control and state parameters of a multi-dimensional complex system, helping us derive effective one-dimensional dynamics that accurately predict the system's resilience. The proposed analytical framework allows us systematically to separate the roles of the system's dynamics and topology, collapsing the behaviour of different networks onto a single universal resilience function. The analytical results unveil the network characteristics that can enhance or diminish resilience, offering ways to prevent the collapse of ecological, biological or economic systems, and guiding the design of technological systems resilient to both internal failures and environmental changes.

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          Most cited references23

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          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.
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            Is Open Access

            Epidemic spreading in scale-free networks

            The Internet, as well as many other networks, has a very complex connectivity recently modeled by the class of scale-free networks. This feature, which appears to be very efficient for a communications network, favors at the same time the spreading of computer viruses. We analyze real data from computer virus infections and find the average lifetime and prevalence of viral strains on the Internet. We define a dynamical model for the spreading of infections on scale-free networks, finding the absence of an epidemic threshold and its associated critical behavior. This new epidemiological framework rationalize data of computer viruses and could help in the understanding of other spreading phenomena on communication and social networks.
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              Network structure and biodiversity loss in food webs: robustness increases with connectance

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                Author and article information

                Journal
                Nature
                Nature
                1476-4687
                0028-0836
                Feb 18 2016
                : 530
                : 7590
                Affiliations
                [1 ] Center for Complex Network Research, Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA.
                [2 ] Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel.
                [3 ] Center for Cancer Systems Biology, Dana-Farber Cancer Institute, Harvard University, Boston, Massachusetts 02215, USA.
                [4 ] Department of Medicine, Brigham and Women's Hospital, Harvard Medical School, Boston, Massachusetts 02115, USA.
                [5 ] Center for Network Science, Central European University, Budapest 1051, Hungary.
                Article
                nature16948
                10.1038/nature16948
                26887493
                f8599f10-8334-4f1f-93b1-f18f64ef633f
                History

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