Structure properties of evolutionary spatially embedded networks

Z. Hui, Wei Li, Xu Cai, J.M. J.M. Greneche, and Q.A. Wang

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Submission date: 17. Dec. 2013
Pages: 13
published in: Physica / A, 392 (2013) 8, p. 1909-1919 
DOI number (of the published article): 10.1016/j.physa.2013.01.002
Bibtex
Keywords and phrases: Euclidean distance preference, Small world network, phase transition
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Abstract:
This work is a modeling of evolutionary networks embedded in one or two dimensional configuration space. The evolution is based on two attachments depending on degree and spatial distance. The probability for a new node n to connect with a previous node i at distance r_ni follows a + (1 -a) , where k_i is the degree of node i, α and a are tunable parameters. In spatial driven model (a = 0), the spatial distance distribution follows the power-law feature. The mean topological distance l and the clustering coefficient C exhibit phase transitions at same critical values of α which change with the dimensionality d of the embedding space. When a ≤ 0, the degree distribution follows the shifted power law (SPL) which interpolates between exponential and scale-free distributions depending on the value of a.