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Science 15 October 1999:
Vol. 286. no. 5439, p. 373
DOI: 10.1126/science.286.5439.373b
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This Week in Science
Networks consist of a number of vertices that are connected to each other by edges in some manner. Barabási and Albert (p. 509) analyzed the structure of some very large networks, including a sample of pages on the World Wide Web (>300,000 vertices), the network of actor collaborations (>200,000 vertices), and the power grid system in western United States (>5000 vertices). They found that the topology of the networks, that is, the probability P that a vertex is connected to k other vertices, can all be described by power laws P(k) = k-g, where g may range from 2.1 to 4. Conventional network analyses predict an exponential relation of the topology rather than a power law, which suggests that vertices with a large number of connections should be absent in very large networks. The model provided here allows the network to grow by adding vertices and prefers to connect new vertices to ones that are already well connected. This model reflects aspects of real-world behavior--for example, people tend to link their new Web page to ones that are already popular.
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Science. ISSN 0036-8075 (print), 1095-9203 (online)
