Evolving networks with disadvantaged long-range connections.
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 alpha is a tunable parameter of the model. We show that the properties of the networks grown with alpha<1 are close to those of the genuine scale-free construction, while for alpha>1 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 alpha.
Xulvi-Brunet
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Institut für Physik, Humboldt Universität zu Berlin, Invalidenstrasse 110, D-10115 Berlin, Germany.
Sokolov
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