### 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 |
---|---|

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 |

### Fingerprint

### 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

**Universal power laws in the threshold network model : A theoretical analysis based on extreme value theory.** / Fujihara, A.; Uchida, Masato; Miwa, H.

Research output: Contribution to journal › Article

*Physica A: Statistical Mechanics and its Applications*, vol. 389, no. 5, pp. 1124-1130. https://doi.org/10.1016/j.physa.2009.11.002

}

TY - JOUR

T1 - Universal power laws in the threshold network model

T2 - A theoretical analysis based on extreme value theory

AU - Fujihara, A.

AU - Uchida, Masato

AU - Miwa, H.

PY - 2010/3/1

Y1 - 2010/3/1

N2 - 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.

AB - 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.

KW - Complex networks

KW - Extreme value theory

KW - Power laws

KW - Threshold network model

UR - http://www.scopus.com/inward/record.url?scp=71649115202&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=71649115202&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2009.11.002

DO - 10.1016/j.physa.2009.11.002

M3 - Article

VL - 389

SP - 1124

EP - 1130

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 5

ER -