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Random initial condition in small Barabasi-Albert networks and deviations from the scale-free behavior

Paulo R. Guimarães, Jr.1,3, Marcus A. M. de Aguiar2, Jordi Bascompte3, Pedro Jordano3, and Sérgio Furtado dos Reis4

  • 1Instituto de Biologia, Universidade Estadual de Campinas (UNICAMP), Caixa Postal 6109, 13083-970 Campinas, SP, Brazil
  • 2Instituto de Física “Gleb Wataghin,” Universidade Estadual de Campinas (UNICAMP), Caixa Postal 6165, 13083-970 Campinas, SP, Brazil
  • 3Integrative Ecology Group, Estación Biológica de Doñana, CSIC, Apdo. 1056, E-41080 Sevilla, Spain
  • 4Departamento de Parasitologia, Instituto de Biologia, Universidade Estadual de Campinas (UNICAMP), Caixa Postal 6109, 13083-970, Campinas, SP, Brazil

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Phys. Rev. E 71, 037101 – Published 18 March, 2005

DOI: https://doi.org/10.1103/PhysRevE.71.037101

Abstract

Barabasi-Albert networks are constructed by adding nodes via preferential attachment to an initial core of nodes. We study the topology of small scale-free networks as a function of the size and average connectivity of their initial random core. We show that these two parameters may strongly affect the tail of the degree distribution, by consistently leading to broad-scale or single-scale networks. In particular, we argue that the size of the initial network core and its density of connections may be the main responsible for the exponential truncation of the power-law behavior observed in some small scale-free networks.

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Phys. Rev. E 71, 037101– Published 18 March, 2005
  • Received 3 November 2004

© 2005 American Physical Society

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