Weighted Scale-free Networks in Euclidean Space Using Local Selection Rule

摘要

A spatial scale-free network is introduced and studied whose motivation hasbeen originated in the growing Internet as well as the Airport networks. Weargue that in these real-world networks a new node necessarily selects one ofits neighbouring local nodes for connection and is not controlled by thepreferential attachment as in the Barab\'asi-Albert (BA) model. Thisobservation has been mimicked in our model where the nodes pop-up at randomlylocated positions in the Euclidean space and are connected to one end of thenearest link. In spite of this crucial difference it is observed that theleading behaviour of our network is like the BA model. Defining link weight asan algebraic power of its Euclidean length, the weight distribution and thenon-linear dependence of the nodal strength on the degree are analyticallycalculated. It is claimed that a power law decay of the link weights with timeensures such a non-linear behavior. Switching off the Euclidean space from thesame model yields a much simpler definition of the Barab\'asi-Albert modelwhere numerical effort grows linearly with $N$.