Self -similarity and scaling theory of complex networks.
Item
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Title
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Self -similarity and scaling theory of complex networks.
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Identifier
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AAI3296953
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identifier
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3296953
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Creator
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Song, Chaoming.
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Contributor
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Adviser: Hernan Makse
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Date
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2008
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Language
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English
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Publisher
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City University of New York.
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Subject
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Physics, Condensed Matter
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Abstract
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Scale-free networks have been studied extensively due to their relevance to many real systems as diverse as the World Wide Web (WWW), the Internet, biological and social networks. We present a novel approach to the analysis of scale-free networks, revealing that their structure is self-similar. This result is achieved by the application of a renormalization procedure which coarse-grains the system into boxes containing nodes within a given "size". Concurrently, we identify a power-law relation between the number of boxes needed to cover the network and the size of the box defining a self-similar exponent, which classifies fractal and non-fractal networks. By using the concept of renormalization as a mechanism for the growth of fractal and non-fractal modular networks, we show that the key principle that gives rise to the fractal architecture of networks is a strong effective "repulsion" between the most connected nodes (hubs) on all length scales, rendering them very dispersed. We show that a robust network comprised of functional modules, such as a cellular network, necessitates a fractal topology, suggestive of a evolutionary drive for their existence. These fundamental properties help to understand the emergence of the scale-free property in complex networks.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
