Scaling properties of d-dimensional complex networks

Samuraí Brito, Thiago C. Nunes, Luciano R. da Silva, and Constantino Tsallis
Phys. Rev. E 99, 012305 – Published 3 January 2019

Abstract

The area of networks is very interdisciplinary and exhibits many applications in several fields of science. Nevertheless, there are few studies focusing on geographically located d-dimensional networks. In this paper, we study the scaling properties of a wide class of d-dimensional geographically located networks which grow with preferential attachment involving Euclidean distances through rijαA (αA0). We have numerically analyzed the time evolution of the connectivity of sites, the average shortest path, the degree distribution entropy, and the average clustering coefficient for d=1,2,3,4 and typical values of αA. Remarkably enough, virtually all the curves can be made to collapse as functions of the scaled variable αA/d. These observations confirm the exist- ence of three regimes. The first one occurs in the interval αA/d[0,1]; it is non-Boltzmannian with very-long-range interactions in the sense that the degree distribution is a q exponential with q constant and above unity. The critical value αA/d=1 that emerges in many of these properties is replaced by αA/d=1/2 for the β exponent which characterizes the time evolution of the connectivity of sites. The second regime is still non-Boltzmannian, now with moderately-long-range interactions, and reflects in an index q monotonically decreasing with αA/d increasing from its critical value to a characteristic value αA/d5. Finally, the third regime is Boltzmannian-like (with q1) and corresponds to short-range interactions.

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  • Received 4 October 2018

DOI:https://doi.org/10.1103/PhysRevE.99.012305

©2019 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsNetworksInterdisciplinary Physics

Authors & Affiliations

Samuraí Brito1,*, Thiago C. Nunes2,†, Luciano R. da Silva2,3,‡, and Constantino Tsallis3,4,5,6,§

  • 1International Institute of Physics, Universidade Federal do Rio Grande do Norte, Campus Universitário, Lagoa Nova, Natal-RN 59078-970, Brazil
  • 2Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Natal, RN, 59078-900, Brazil
  • 3National Institute of Science and Technology of Complex Systems, Brazil
  • 4Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro-RJ, Brazil
  • 5Santa Fe Institute, 1399 Hyde Park Road, New Mexico 87501, USA
  • 6Complexity Science Hub Vienna, Josefstaedter Strasse 39, A 1080 Vienna, Austria

  • *samuraigab@gmail.com.br
  • thiago.cris@yahoo.com.br
  • luciano@fisica.ufrn.br
  • §tsallis@cbpf.br

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Issue

Vol. 99, Iss. 1 — January 2019

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