Volume 70, Number 1, April 2005
|Page(s)||70 - 76|
|Published online||09 March 2005|
Preferential attachment growth model and nonextensive statistical mechanics
Departamento de Física Teórica e Experimental Universidade Federal do Rio Grande do Norte Campus Universitario, 59072-970 Natal-RN, Brazil
2 Departamento de Física, Universidade Federal do Ceará 60451-970, Fortaleza-Ce, Brazil
3 Centro Brasileiro de Pesquisas Físicas - Rua Xavier Sigaud 150 22290-180 Rio de Janeiro-RJ, Brazil
4 Santa Fe Institute - 1399 Hyde Park Road, Santa Fe, NM 87501, USA
Accepted: 8 February 2005
We introduce a two-dimensional growth model where every new site is located, at a distance r from the barycenter of the pre-existing graph, according to the probability law , and is attached to (only) one pre-existing site with a probability (; ki is the number of links of the i-th site of the pre-existing graph, and ri its distance to the new site). Then we numerically determine that the probability distribution for a site to have k links is asymptotically given, for all values of , by , where is the function naturally emerging within nonextensive statistical mechanics. The entropic index is numerically given (at least for not too large) by , and the characteristic number of links by . The particular case belongs to the same universality class to which the Barabasi-Albert model belongs. In addition to this, we have numerically studied the rate at which the average number of links increases with the scaled time ; asymptotically, , the exponent being close to for , and zero otherwise. The present results reinforce the conjecture that the microscopic dynamics of nonextensive systems typically build (for instance, in Gibbs Γ-space for Hamiltonian systems) a scale-free network.
PACS: 05.70.Ln – Nonequilibrium and irreversible thermodynamics / 89.75.Hc – Networks and genealogical trees / 89.75.-k – Complex systems
© EDP Sciences, 2005
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