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Cut-offs and finite size effects in scale-free networks

Abstract.

We analyze the degree distribution’s cut-off in finite size scale-free networks. We show that the cut-off behavior with the number of vertices N is ruled by the topological constraints induced by the connectivity structure of the network. Even in the simple case of uncorrelated networks, we obtain an expression of the structural cut-off that is smaller than the natural cut-off obtained by means of extremal theory arguments. The obtained results are explicitly applied in the case of the configuration model to recover the size scaling of tadpoles and multiple edges.

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Correspondence to M. Boguñá.

Additional information

Received: 18 November 2003, Published online: 24 February 2004

PACS:

89.75.-k Complex systems - 87.23.Ge Dynamics of social systems - 05.70.Ln Nonequilibrium and irreversible thermodynamics

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Boguñá, M., Pastor-Satorras, R. & Vespignani, A. Cut-offs and finite size effects in scale-free networks. Eur. Phys. J. B 38, 205–209 (2004). https://doi.org/10.1140/epjb/e2004-00038-8

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Keywords

  • Degree Distribution
  • Finite Size
  • Configuration Model
  • Connectivity Structure
  • Multiple Edge