Weighted scale-free networks in Euclidean space using local selection rule

A spatial scale-free network is introduced and studied, whose motivation originated in the growing Internet as well as airport networks. We argue that in these real-world networks a new node necessarily selects one of its neighboring local nodes for connection and is not controlled by preferential attachment as in the Barabási-Albert (BA) model. This observation is mimicked in our model where the nodes pop up at randomly located positions in the Euclidean space and are connected to one end of the nearest link. In spite of this crucial difference it is observed that the leading behavior of our network is like that of the BA model. Defining the link weight as an algebraic power of its Euclidean length, the weight distribution and the nonlinear dependence of the nodal strength on the degree are analytically calculated. It is claimed that a power law decay of the link weights with time ensures such nonlinear behavior. Switching off the Euclidean space from the same model yields a much simpler definition of the BA model where numerical effort grows linearly with $N$.