### Abstract

Motivated by the hierarchial network model of E. Ravasz, A.-L. Barabási, and T. Vicsek, we introduce deterministic scale-free networks derived from a graph directed self-similar fractal Λ. With rigorous mathematical results we verify that our model captures some of the most important features of many real networks: the scale-free and the high clustering properties. We also prove that the diameter is the logarithm of the size of the system. We point out a connection between the power law exponent of the degree distribution and some intrinsic geometric measure theoretical properties of the underlying fractal. Using our (deterministic) fractal Λ we generate random graph sequence sharing similar properties.

Original language | English |
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Pages (from-to) | 651-666 |

Number of pages | 16 |

Journal | Chaos, Solitons and Fractals |

Volume | 44 |

Issue number | 8 |

DOIs | |

Publication status | Published - Aug 2011 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Chaos, Solitons and Fractals*,

*44*(8), 651-666. https://doi.org/10.1016/j.chaos.2011.05.012

**Generating hierarchial scale-free graphs from fractals.** / Komjáthy, Júlia; Simon, K.

Research output: Contribution to journal › Article

*Chaos, Solitons and Fractals*, vol. 44, no. 8, pp. 651-666. https://doi.org/10.1016/j.chaos.2011.05.012

}

TY - JOUR

T1 - Generating hierarchial scale-free graphs from fractals

AU - Komjáthy, Júlia

AU - Simon, K.

PY - 2011/8

Y1 - 2011/8

N2 - Motivated by the hierarchial network model of E. Ravasz, A.-L. Barabási, and T. Vicsek, we introduce deterministic scale-free networks derived from a graph directed self-similar fractal Λ. With rigorous mathematical results we verify that our model captures some of the most important features of many real networks: the scale-free and the high clustering properties. We also prove that the diameter is the logarithm of the size of the system. We point out a connection between the power law exponent of the degree distribution and some intrinsic geometric measure theoretical properties of the underlying fractal. Using our (deterministic) fractal Λ we generate random graph sequence sharing similar properties.

AB - Motivated by the hierarchial network model of E. Ravasz, A.-L. Barabási, and T. Vicsek, we introduce deterministic scale-free networks derived from a graph directed self-similar fractal Λ. With rigorous mathematical results we verify that our model captures some of the most important features of many real networks: the scale-free and the high clustering properties. We also prove that the diameter is the logarithm of the size of the system. We point out a connection between the power law exponent of the degree distribution and some intrinsic geometric measure theoretical properties of the underlying fractal. Using our (deterministic) fractal Λ we generate random graph sequence sharing similar properties.

UR - http://www.scopus.com/inward/record.url?scp=79960801242&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79960801242&partnerID=8YFLogxK

U2 - 10.1016/j.chaos.2011.05.012

DO - 10.1016/j.chaos.2011.05.012

M3 - Article

AN - SCOPUS:79960801242

VL - 44

SP - 651

EP - 666

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

SN - 0960-0779

IS - 8

ER -