## Abstract

Network theory is a powerful tool for describing and modeling complex systems having applications in widelydiffering areas including epidemiology [16], neuroscience [34], ecology [20] and the Internet [26]. In its beginning, one often compared an empirically given network, whose nodes are the elements of the system and whose edges represent their interactions, with an ensemble having the same number of nodes and edges, the most popular example being the random graphs introduced by Erdos and Renyi [11]. As the field matured, it became clear that the naive model above needed to be refined, due to the observation that real-world networks often differ significantly from the Erdos–Renyi random graphs in having a highly heterogenous non-Poisson degree distribution [5, 15] and in possessing a high level of clustering [33]. Methods for generating random networks with arbitrary degree distributions and for calculating their statistical properties are now well understood.

Original language | English |
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Title of host publication | Modeling and Simulation in Science, Engineering and Technology |

Publisher | Springer Basel |

Pages | 237-252 |

Number of pages | 16 |

DOIs | |

State | Published - 2009 |

### Publication series

Name | Modeling and Simulation in Science, Engineering and Technology |
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Volume | 42 |

ISSN (Print) | 2164-3679 |

ISSN (Electronic) | 2164-3725 |

### Bibliographical note

Funding Information:MT and YB are grateful for the support of the EC (project MATHfSS 15661) and DIP (project Compositionality F 1.2). LS and YAR are grateful for the support of the James S. McDonnell Foundation and the Israeli Science Foundation.

Publisher Copyright:

© Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2009.