Emergence of scaling in random networks.

*(English)*Zbl 1226.05223Summary: 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 |