Scale-free network on a vertical plane

Details Scale-free network on a vertical plane Scale-free network on a vertical plane

2003-07-07

arxiv.org/abs/cond-mat/0307137v1

Phys. Rev. E 69, 017102 (2004)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 4 figures

Scientific paper

10.1103/PhysRevE.69.017102

A scale-free network is grown in the Euclidean space with a global directional bias. On a vertical plane, nodes are introduced at unit rate at randomly selected points and a node is allowed to be connected only to the subset of nodes which are below it using the attachment probability: $\pi_i(t) \sim k_i(t)\ell^{\alpha}$. Our numerical results indicate that the directed scale-free network for $\alpha=0$ belongs to a different universality class compared to the isotropic scale-free network. For $\alpha < \alpha_c$ the degree distribution is stretched exponential in general which takes a pure exponential form in the limit of $\alpha \to -\infty$. The link length distribution is calculated analytically for all values of $\alpha$.

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