Evolving networks with disadvantaged long-range connections

Abstract

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 to get 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 vastly different. Thus, in this regime, the node degree distribution is no more 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 $\alpha$.

REVTeX, 6 pages, 5 figures

References in corpus (7)

• Statistical mechanics of complex networks
• Lethality and centrality in protein networks
• Evolution of networks
• Who is the best connected scientist? A study of scientific coauthorship networks
• The Web of Human Sexual Contacts
• Preferencial growth: exact solution of the time dependent distributions
• Exact solutions of epidemic models on networks

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