9,903 research outputs found

    Spatial preferential attachment networks: Power laws and clustering coefficients

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    We define a class of growing networks in which new nodes are given a spatial position and are connected to existing nodes with a probability mechanism favoring short distances and high degrees. The competition of preferential attachment and spatial clustering gives this model a range of interesting properties. Empirical degree distributions converge to a limit law, which can be a power law with any exponent Ď„>2\tau>2. The average clustering coefficient of the networks converges to a positive limit. Finally, a phase transition occurs in the global clustering coefficients and empirical distribution of edge lengths when the power-law exponent crosses the critical value Ď„=3\tau=3. Our main tool in the proof of these results is a general weak law of large numbers in the spirit of Penrose and Yukich.Comment: Published in at http://dx.doi.org/10.1214/14-AAP1006 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Evolution of the social network of scientific collaborations

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    The co-authorship network of scientists represents a prototype of complex evolving networks. By mapping the electronic database containing all relevant journals in mathematics and neuro-science for an eight-year period (1991-98), we infer the dynamic and the structural mechanisms that govern the evolution and topology of this complex system. First, empirical measurements allow us to uncover the topological measures that characterize the network at a given moment, as well as the time evolution of these quantities. The results indicate that the network is scale-free, and that the network evolution is governed by preferential attachment, affecting both internal and external links. However, in contrast with most model predictions the average degree increases in time, and the node separation decreases. Second, we propose a simple model that captures the network's time evolution. Third, numerical simulations are used to uncover the behavior of quantities that could not be predicted analytically.Comment: 14 pages, 15 figure

    Power Grid Network Evolutions for Local Energy Trading

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    The shift towards an energy Grid dominated by prosumers (consumers and producers of energy) will inevitably have repercussions on the distribution infrastructure. Today it is a hierarchical one designed to deliver energy from large scale facilities to end-users. Tomorrow it will be a capillary infrastructure at the medium and Low Voltage levels that will support local energy trading among prosumers. In our previous work, we analyzed the Dutch Power Grid and made an initial analysis of the economic impact topological properties have on decentralized energy trading. In this paper, we go one step further and investigate how different networks topologies and growth models facilitate the emergence of a decentralized market. In particular, we show how the connectivity plays an important role in improving the properties of reliability and path-cost reduction. From the economic point of view, we estimate how the topological evolutions facilitate local electricity distribution, taking into account the main cost ingredient required for increasing network connectivity, i.e., the price of cabling

    Statistical mechanics of complex networks

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    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.Comment: 54 pages, submitted to Reviews of Modern Physic
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