Modulated Scale-free Network in the Euclidean Space

Details Modulated Scale-free Network in the Euclidean Space Modulated Scale-free Network in the Euclidean Space

2002-03-10

arxiv.org/abs/cond-mat/0203216v2

Phys. Rev. E. 66, 066114 (2002)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 4 figures. To be published in Physical Review E

Scientific paper

10.1103/PhysRevE.66.066114

A random network is grown by introducing at unit rate randomly selected nodes on the Euclidean space. A node is randomly connected to its $i$-th predecessor of degree $k_i$ with a directed link of length $\ell$ using a probability proportional to $k_i \ell^{\alpha}$. Our numerical study indicates that the network is Scale-free for all values of $\alpha > \alpha_c $ and the degree distribution decays stretched exponentially for the other values of $\alpha$. The link length distribution follows a power law: $D(\ell) \sim \ell^{\delta}$ where $\delta$ is calculated exactly for the whole range of values of $\alpha$.

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