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Emergence of scaling in random networks. (English) Zbl 1226.05223
Summary: Systems as diverse as genetic networks or the World Wide Web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This feature was found to be a consequence of two generic mechanisms: (i) networks expand continuously by the addition of new vertices, and (ii) new vertices attach preferentially to sites that are already well connected. A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.

MSC:
05C80 Random graphs (graph-theoretic aspects)
68R10 Graph theory (including graph drawing) in computer science
68U35 Computing methodologies for information systems (hypertext navigation, interfaces, decision support, etc.)
82C44 Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics
94C99 Circuits, networks
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