1999/03/05 by Marc Barthélemy, Marc Barthelemy, Luı́s A. Nunes Amaral +1 · 5 citations
Mathematics · Physics and Astronomy · #Approx #Artificial intelligence #Combinatorics #Complex Network Analysis Techniques #Complex network #Computer science #Crossover #Degree (music) #Function (biology) #Length scale #Mathematics #Opinion Dynamics and Social Influence #Physics #Quantum mechanics #Scale (ratio) #Scaling #Small-world network #Statistical physics #Theoretical and Computational Physics #adap-org #cond-mat.dis-nn #cond-mat.stat-mech #nlin.AO
paper · pdf · doi:10.1103/physrevlett.82.3180
5 pages, 5 postscript figures (1 in color), Latex/Revtex/multicols/epsf. Accepted for publication in Physical Review Letters
arxiv created 1999/03/05 · openalex publication_date 1999/04/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Watts and Strogatz [Nature (London) 393, 440 (1998)] have recently introduced a model for disordered networks and reported that, even for very small values of the disorder p in the links, the network behaves as a ``small world.'' Here, we test the hypothesis that the appearance of small-world behavior is not a phase transition but a crossover phenomenon which depends both on the network size n and on the degree of disorder p. We propose that the average distance \ensuremathℓ between any two vertices of the network is a scaling function of n/n*. The crossover size n* above which the network behaves as a small world is shown to scale as n*(p\ensuremath≪1)\ensuremath∼p^\ensuremath-\ensuremathτ with \ensuremathτ\ensuremath≈2/3.