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What is Scale-Free Network

Encyclopedia of Networked and Virtual Organizations
A network that contains hubs, that is, vertices which have a seemingly unlimited number of links and in which no vertex is typical of the others. Scale-free networks are remarkably resistant to accidental failures but extremely vulnerable to coordinated attacks. The scale-free model assumes that the network grows continuously by adding new vertices. New vertices would connect with higher probability to higher connected vertices, a phenomenon called preferential attachment.
Published in Chapter:
Measures of Network Structure
Ani Calinescu (Oxford University Computing Laboratory, UK) and Janet Efstathiou (Oxford University Business School, UK)
Copyright: © 2008 |Pages: 7
DOI: 10.4018/978-1-59904-885-7.ch122
Abstract
Networked systems, natural or designed, have always been part of life. Their sophistication degree and complexity have increased through either natural evolution or technological progress. However, recent theoretical results have shown that a previously unexpected number of different classes of networks share similar network architectures and universal laws. Examples of such networks include metabolic pathways and ecosystems, the Internet and the World Wide Web, and organizational, social, and neural networks. Complex systems-related research questions investigated by researchers nowadays include: how consciousness arises out of the interactions of the neurons in the brain and between the brain and the environment (Amaral & Ottino, 2004; Barabási, 2005; Barabási & Oltvai, 2004; Neuman, 2003b) and how this understanding could be used for designing networked organizations or production networks whose behavior satisfies a given specification.
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Rich-Club Phenomenon of the Internet Topology
A network characterised by a power-law distribution of node degree, where the power-law exponent is invariant to the network size (scale).
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Clique Size and Centrality Metrics for Analysis of Real-World Network Graphs
A network whose degree distribution follows a power-law pattern wherein a majority of the vertices have a smaller degree, but there exists a non-zero probability for finding a vertex with a relatively much larger degree.
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Positive-Feedback Preference Model of the Internet Topology
A network characterized by a power-law distribution of node degree, where the power-law exponent is invariant to the network size (scale).
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Discovery and Existence of Communities in the World Wide Web
A network is characterized as scale-free if the distribution of degrees of its vertices follows a power-law for large k, like the following P(k) ~ k-?. Simply stated, some vertices of such a network are highly connected while others have few connections.
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