We consider a growing network, whose growth algorithm is based on the preferential attachment typical for scale-free constructions, but where the long-range bonds are disadvantaged. Thus, the probability of getting connected to a site at distance d is proportional to $d^{-\alpha },$ where α is a tunable parameter of the model. We show that the properties of the networks grown with $\alpha <1\mathrm{}$ are close to those of the genuine scale-free construction, while for $\alpha >1\mathrm{}$ the structure of the network is quite different. Thus, in this regime, the node degree distribution is no longer a power law, and it is well represented by a stretched exponential. On the other hand, the small-world property of the growing networks is preserved at all values of α.

• Received 7 May 2002

DOI:https://doi.org/10.1103/PhysRevE.66.026118