ARTÍCULO
On the Emergence of Islands in Complex Networks
J. Esquivel-Gómez, R. E. Balderas-Navarro, P. D. Arjona-Villicaña, P. Castillo-Castillo, O. Rico-Trejo, and J. Acosta-Elias
Complexity, Volume 2017 (2017), Article ID 7157943,
https://doi.org/10.1155/2017/7157943, 2017.
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 (𝐼𝑠) obeying a power-law function 𝐼𝑠 ∼ 𝑠−𝛼. 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 𝐼𝑠 ∼ 𝑠−𝛼 with a fixed exponent 𝛼=1 and in-degree distribution that decays as a power-law 𝑄𝑖 ∼ 𝑖−𝛾 with 𝛾=2. When the second case is considered, the model describes island size and in-degree distributions that decay as a power-law with 2<𝛼<∞ and 2<𝛾<∞, respectively.