### Abstract

The most general form of the Aboav-Weaire empirical topological law of random cellular networks is derived from conditions on local averages in two dimensions. We assume the average number of edges in a local cluster depends on the number of actual edges and its moments together with the probability distribution function. Based on this constitutive assumption we show that the Aboav-Weaire law depends only on the first and second moments of the distribution function. We show that the Aboav-Weaire law is a direct consequence of the existence of the well-known microscopic topological transformations. We study the effect of the constitutive equation's coefficients on the Aboav-Weaire law. The properties near to the equilibrium are also investigated to explain the role of the actual parameters of the network.

Original language | English |
---|---|

Pages (from-to) | 1-12 |

Number of pages | 12 |

Journal | Journal of Geometry and Physics |

Volume | 51 |

Issue number | 1 |

DOIs | |

Publication status | Published - May 2004 |

### Fingerprint

### Keywords

- Cellular networks

### ASJC Scopus subject areas

- Geometry and Topology
- Mathematical Physics
- Physics and Astronomy(all)

### Cite this

*Journal of Geometry and Physics*,

*51*(1), 1-12. https://doi.org/10.1016/j.geomphys.2003.08.003

**On the Aboav-Weaire law.** / Vincze, Gy; Zsoldos, I.; Szász, A.

Research output: Contribution to journal › Article

*Journal of Geometry and Physics*, vol. 51, no. 1, pp. 1-12. https://doi.org/10.1016/j.geomphys.2003.08.003

}

TY - JOUR

T1 - On the Aboav-Weaire law

AU - Vincze, Gy

AU - Zsoldos, I.

AU - Szász, A.

PY - 2004/5

Y1 - 2004/5

N2 - The most general form of the Aboav-Weaire empirical topological law of random cellular networks is derived from conditions on local averages in two dimensions. We assume the average number of edges in a local cluster depends on the number of actual edges and its moments together with the probability distribution function. Based on this constitutive assumption we show that the Aboav-Weaire law depends only on the first and second moments of the distribution function. We show that the Aboav-Weaire law is a direct consequence of the existence of the well-known microscopic topological transformations. We study the effect of the constitutive equation's coefficients on the Aboav-Weaire law. The properties near to the equilibrium are also investigated to explain the role of the actual parameters of the network.

AB - The most general form of the Aboav-Weaire empirical topological law of random cellular networks is derived from conditions on local averages in two dimensions. We assume the average number of edges in a local cluster depends on the number of actual edges and its moments together with the probability distribution function. Based on this constitutive assumption we show that the Aboav-Weaire law depends only on the first and second moments of the distribution function. We show that the Aboav-Weaire law is a direct consequence of the existence of the well-known microscopic topological transformations. We study the effect of the constitutive equation's coefficients on the Aboav-Weaire law. The properties near to the equilibrium are also investigated to explain the role of the actual parameters of the network.

KW - Cellular networks

UR - http://www.scopus.com/inward/record.url?scp=1842449713&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1842449713&partnerID=8YFLogxK

U2 - 10.1016/j.geomphys.2003.08.003

DO - 10.1016/j.geomphys.2003.08.003

M3 - Article

AN - SCOPUS:1842449713

VL - 51

SP - 1

EP - 12

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

SN - 0393-0440

IS - 1

ER -