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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:
05C80Random graphs
68R10Graph theory in connection with computer science (including graph drawing)
68U35Information systems (hypertext navigation, interfaces, decision support, etc.)
82C44Dynamics of disordered systems (random Ising systems, etc.)
94C99Circuits, networks