Preferential Attachment Scale-Free Growth Model with Random Fitness and Connection with Tsallis Statistics(COMPLEXITY AND NONEXTENSIVITY:NEW TRENDS IN STATISTICAL MECHANICS)

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概要

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• We introduce a model which consists in a planar network which grows by adding nodes at a distance r from the pre-existing barycenter. Each new node position is randomly located through the distribution law P(r) ∝ 1/r^γ with γ>1. The new node j is linked to only one pre-existing node according to the probability law [numerical formula]; k_i is the number of links of the i^<th> node, η_i is its fitness (or quality factor), and r_<ij> is the distance. We consider in the present paper two models for η_i. In one of them, the single fitness model (SFM [D. J. B. Soares, C. Tsallis, A. M. Mariz and L. R. da Silva, Europhys. Lett. 70 (2005), 70.]), we consider [numerical formula]. In the other one, the uniformly distributed fitness model (UDFM), η_i is chosen to be uniformly distributed within the interval (0, 1]. We have determined numerically the degree distribution P(k). This distribution appears to be well fitted with [numerical formula] with q≥1, where [numerical formula] is the q-exponential function naturally emerging within Tsallis nonextensive statistical mechanics. We determine, for both models, the entropic index q as a function of αA. Additionally, we determine the average topological (or chemical) distance within the network, and the time evolution of the average number of links <k_i>. We obtain that, asymptotically, <k_i> ∝ (t/i)^β, (i coincides with the input-time of the i^<th> node) and β(αA) to both cases.

• 理論物理学刊行会の論文
• 2006-06-05

著者

• Cunha Sharon

  Departamento De Fisica Teorica E Experimental Universidade Federal Do Rio Grande Do Norte Campus Uni

• Da Cunha

  Departamento De Fisica Teorica E Experimental Universidade Federal Do Rio Grande Do Norte

• MENESES Marcelo

  Departamento de Fisica Teorica e Experimental, Universidade Federal do Rio Grande do Norte, Campus U

• SCARES Danyel

  Departamento de Fisica Teorica e Experimental, Universidade Federal do Rio Grande do Norte, Campus U

• SILVA Luciano

  Departamento de Fisica Teorica e Experimental, Universidade Federal do Rio Grande do Norte, Campus U

• Silva Luciano

  Departamento De Fisica Teorica E Experimental Universidade Federal Do Rio Grande Do Norte Campus Uni

• Scares Danyel

  Departamento De Fisica Teorica E Experimental Universidade Federal Do Rio Grande Do Norte Campus Uni

• Meneses Marcelo

  Departamento De Fisica Teorica E Experimental Universidade Federal Do Rio Grande Do Norte Campus Uni

• De Meneses

  Departamento De Fisica Teorica E Experimental Universidade Federal Do Rio Grande Do Norte

• SILVA Luciano

  Departamento de Fisica Teorica e Experimental, Universidade Federal do Rio Grande do Norte, Campus Universitario

• CUNHA Sharon

  Departamento de Fisica Teorica e Experimental, Universidade Federal do Rio Grande do Norte, Campus Universitario

• MENESES Marcelo

  Departamento de Fisica Teorica e Experimental, Universidade Federal do Rio Grande do Norte, Campus Universitario

• Soares Danyel

  Departamento de Fisica Teorica e Experimental, Universidade Federal do Rio Grande do Norte, Campus Universitario

• Soares Danyel

  Departamento de Fisica Teorica e Experimental, Universidade Federal do Rio Grande do Norte, Campus Universitario:Departamento de Biofisica e Farmacologia, Centro de Biociencias, Universidade Federal do Rio Grande do Norte, Campus Universitario

関連論文

• Preferential Attachment Scale-Free Growth Model with Random Fitness and Connection with Tsallis Statistics(COMPLEXITY AND NONEXTENSIVITY:NEW TRENDS IN STATISTICAL MECHANICS)
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