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MiS Preprint
113/2013

Structure properties of evolutionary spatially embedded networks

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

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 $a \frac{k_i}{\sum_j k_j}+(1-a)\frac{r^{-\alpha}_{ni}}{\sum_j r^{-\alpha}_{nj}}$, where $k_i$ is the degree of node $i$, $\alpha$ 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 $\alpha$ which change with the dimensionality d of the embedding space. When $a \le 0$, the degree distribution follows the "shifted power law" (SPL) which interpolates between exponential and scale-free distributions depending on the value of $a$.

Received:
Dec 17, 2013
Published:
Dec 17, 2013
Keywords:
Euclidean distance preference, Small world network, phase transition

Related publications

inJournal
2013 Repository Open Access
Z. Hui, Wei Li, Xu Cai, J.M. J.M. Greneche and Q.A. Wang

Structure properties of evolutionary spatially embedded networks

In: Physica / A, 392 (2013) 8, pp. 1909-1919