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Complexity
Volume 2017, Article ID 7157943, 10 pages
https://doi.org/10.1155/2017/7157943
Research Article

On the Emergence of Islands in Complex Networks

1Instituto de Investigación en Comunicación Óptica (IICO), Universidad Autónoma de San Luis Potosí (UASLP), San Luis Potosí, SLP, Mexico
2Facultad de Ingeniería, Universidad Autónoma de San Luis Potosí (UASLP), San Luis Potosí, SLP, Mexico
3Facultad de Ciencias, Universidad Autónoma de San Luis Potosí (UASLP), San Luis Potosí, SLP, Mexico
4Universidad Politécnica de San Luis Potosí (UPSLP), San Luis Potosí, SLP, Mexico

Correspondence should be addressed to J. Esquivel-Gómez; xm.plsau.cf@leviuqsej

Received 6 July 2016; Revised 9 November 2016; Accepted 12 December 2016; Published 16 January 2017

Academic Editor: Pietro De Lellis

Copyright © 2017 J. Esquivel-Gómez et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Most growth models for complex networks consider networks comprising a single connected block or island, which contains all the nodes in the network. However, it has been demonstrated that some large complex networks have more than one island, with an island size distribution () obeying a power-law function . This paper introduces a growth model that considers the emergence of islands as the network grows. The proposed model addresses the following two features: (i) the probability that a new island is generated decreases as the network grows and (ii) new islands are created with a constant probability at any stage of the growth. In the first case, the model produces an island size distribution that decays as a power-law with a fixed exponent and in-degree distribution that decays as a power-law with . When the second case is considered, the model describes island size and in-degree distributions that decay as a power-law with and , respectively.