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

2003/11/30 by Marian Boguna, M. Boguñá, Romualdo Pastor-Satorras +3 · 2 citations
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn

paper · pdf · doi:10.1140/epjb/e2004-00038-8

published as Eur. Phys. J. B 38, 205 (2004) · 5 pages, 2 figures. To appear in EPJB

arxiv created 2004/01/15 · openalex publication_date 2004/03/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/01

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 that 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.

Citations

• Detection of topological patterns in complex networks: correlation profile of the internet
• Dynamical and Correlation Properties of the Internet
• Emergence of scaling in random networks
• Assortative Mixing in Networks
• Statistical mechanics of complex networks
• Resilience to damage of graphs with degree correlations
• Evolution of networks

Cited by

• Network coordination and synchronization in a noisy environment with time delays
• Clustering in complex networks. I. General formalism