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      Modeling cascading failures in the North American power grid

      , ,   ,
      The European Physical Journal B
      Springer Science and Business Media LLC

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          Efficient Behavior of Small-World Networks

          We introduce the concept of efficiency of a network as a measure of how efficiently it exchanges information. By using this simple measure, small-world networks are seen as systems that are both globally and locally efficient. This gives a clear physical meaning to the concept of "small world," and also a precise quantitative analysis of both weighted and unweighted networks. We study neural networks and man-made communication and transportation systems and we show that the underlying general principle of their construction is in fact a small-world principle of high efficiency.
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            Finding and evaluating community structure in networks.

            We propose and study a set of algorithms for discovering community structure in networks-natural divisions of network nodes into densely connected subgroups. Our algorithms all share two definitive features: first, they involve iterative removal of edges from the network to split it into communities, the edges removed being identified using any one of a number of possible "betweenness" measures, and second, these measures are, crucially, recalculated after each removal. We also propose a measure for the strength of the community structure found by our algorithms, which gives us an objective metric for choosing the number of communities into which a network should be divided. We demonstrate that our algorithms are highly effective at discovering community structure in both computer-generated and real-world network data, and show how they can be used to shed light on the sometimes dauntingly complex structure of networked systems.
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              Universal Behavior of Load Distribution in Scale-Free Networks

              We study a problem of data packet transport in scale-free networks whose degree distribution follows a power law with the exponent gamma. Load, or "betweenness centrality," of a vertex is the accumulated total number of data packets passing through that vertex when every pair of vertices sends and receives a data packet along the shortest path connecting the pair. It is found that the load distribution follows a power law with the exponent delta approximately 2.2(1), insensitive to different values of gamma in the range, 2 < gamma < or = 3, and different mean degrees, which is valid for both undirected and directed cases. Thus, we conjecture that the load exponent is a universal quantity to characterize scale-free networks.
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                Author and article information

                Journal
                The European Physical Journal B
                Eur. Phys. J. B
                Springer Science and Business Media LLC
                1434-6028
                1434-6036
                July 2005
                August 8 2005
                July 2005
                : 46
                : 1
                : 101-107
                Article
                10.1140/epjb/e2005-00237-9
                34690541
                b6800980-f61f-4546-9488-8d97c3be2635
                © 2005

                http://www.springer.com/tdm

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