Scale-free network on a vertical plane.
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) approximately k(i)(t)l(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-->- infinity. The link length distribution is calculated analytically for all values of alpha.
Satyendra Nath Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700098, India. manna@boson.bose.res.in
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