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

By Marián Boguñá, Romualdo Pastor-Satorras, Alessandro Vespignani. 2003

285 citations recorded by the source corpus.

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.

Subfields: Condensed Matter Physics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/7689f1c7a902f7ea1b555bd1ba3bcc369ba51e22

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In Condensed Matter Physics

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Systematic topology analysis and generation using degree correlations (2006, background): “The two become identical when n → ∞; see [3] for further details.”
Popularity versus similarity in growing networks (2011, background): “1 are due to the increasingly pronounced finite-size effects at γ → 2 [48].”
Critical phenomena in complex networks (2007, background): “(i) When the mean degree is lower than some critical value qc (which is determined by the form of f(q)), the degree distribution P (q) is an exponentially decreasing function.”
Structure and Dynamics of Networks (2009, background): “(2.28) However, the resulting correlation function f(j, k) is still constrained by even further conditions [Boguñá et al., 2004, Dorogovtsev et al., 2005a, Lee et al., 2006].”