### Abstract

We theoretically and numerically investigated the threshold network model with a generic weight function where there were a large number of nodes and a high threshold. Our analysis was based on extreme value theory, which gave us a theoretical understanding of the distribution of independent and identically distributed random variables within a sufficiently high range. Specifically, the distribution could be generally expressed by a generalized Pareto distribution, which enabled us to formulate the generic weight distribution function. By using the theorem, we obtained the exact expressions of degree distribution and clustering coefficient which behaved as universal power laws within certain ranges of degrees. We also compared the theoretical predictions with numerical results and found that they were extremely consistent.

Original language | English |
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Pages (from-to) | 1124-1130 |

Number of pages | 7 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 389 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2010 Mar 1 |

Externally published | Yes |

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### Keywords

- Complex networks
- Extreme value theory
- Power laws
- Threshold network model

### ASJC Scopus subject areas

- Condensed Matter Physics
- Statistics and Probability

### Cite this

*Physica A: Statistical Mechanics and its Applications*,

*389*(5), 1124-1130. https://doi.org/10.1016/j.physa.2009.11.002