### Abstract

In this study we introduce and analyze the statistical structural properties of a model of growing networks which may be relevant to social networks. At each step a new node is added which selects k possible partners from the existing network and joins them with probability delta by undirected edges. The "activity" of the node ends here; it will get new partners only if it is selected by a newcomer. The model produces an infinite-order phase transition when a giant component appears at a specific value of delta, which depends on k. The average component size is discontinuous at the transition. In contrast, the network behaves significantly different for k=1. There is no giant component formed for any delta and thus in this sense there is no phase transition. However, the average component size diverges for delta> or =1/2.

Original language | English |
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Article number | 066104 |

Pages (from-to) | 9 |

Number of pages | 1 |

Journal | Physical review. E, Statistical, nonlinear, and soft matter physics |

Volume | 68 |

Issue number | 6 |

DOIs | |

Publication status | Published - Dec 1 2003 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

### Cite this

*Physical review. E, Statistical, nonlinear, and soft matter physics*,

*68*(6), 9. [066104]. https://doi.org/10.1103/PhysRevE.68.066104