## Abstract

Growing networks have a causal structure. We show that the causality strongly influences the scaling and geometrical properties of the network. In particular the average distance between nodes is smaller for causal networks than for corresponding homogeneous networks. We explain the origin of this effect and illustrate it using as an example a solvable model of random trees. We also discuss the issue of stability of the scale-free node degree distribution. We show that a surplus of links may lead to the emergence of a singular node with the degree proportional to the total number of links. This effect is closely related to the backgammon condensation known from the balls-in-boxes model.

Original language | English |
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Title of host publication | Science of Complex Networks: From Biology to the Internet and WWW |

Editors | JFF Mendes, SN Dorogovtsev, A Povolotsky, FV Abreu, JG Oliveira |

Place of Publication | MELVILLE |

Publisher | American Institute of Physics |

Pages | 14-28 |

Number of pages | 15 |

ISBN (Print) | 0-7354-0262-0 |

Publication status | Published - 2005 |

Event | International Conference on Sciences of Complex Networks - From Biology to the Internet and WWW - Aveiro Duration: 29 Aug 2004 → 2 Sep 2004 |

### Conference

Conference | International Conference on Sciences of Complex Networks - From Biology to the Internet and WWW |
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City | Aveiro |

Period | 29/08/04 → 2/09/04 |

## Keywords

- complex networks
- causality
- statistical ensembles
- scaling properties
- STATISTICAL-MECHANICS
- BRANCHED POLYMERS
- COMPLEX NETWORKS
- MODEL
- EVOLUTION