Abstract
Watts and Strogatz [Nature 393, 440 (1998)] have recently introduced a model\nfor disordered networks and reported that, even for very small values of the\ndisorder $p$ in the links, the network behaves as a small-world. Here, we test\nthe hypothesis that the appearance of small-world behavior is not a\nphase-transition but a crossover phenomenon which depends both on the network\nsize $n$ and on the degree of disorder $p$. We propose that the average\ndistance $\\ell$ between any two vertices of the network is a scaling function\nof $n / n^*$. The crossover size $n^*$ above which the network behaves as a\nsmall-world is shown to scale as $n^*(p \\ll 1) \\sim p^{-\\tau}$ with $\\tau\n\\approx 2/3$.\n
Keywords
CrossoverSmall-world networkScalingPhysicsApproxDegree (music)Length scaleScale (ratio)Function (biology)Statistical physicsCombinatoricsComplex networkMathematicsQuantum mechanicsComputer scienceArtificial intelligence
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Publication Info
- Year
- 1999
- Type
- article
- Volume
- 82
- Issue
- 15
- Pages
- 3180-3183
- Citations
- 297
- Access
- Closed
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Cite This
Marc Barthélémy,
Luı́s A. Nunes Amaral
(1999).
Small-World Networks: Evidence for a Crossover Picture.
Physical Review Letters
, 82
(15)
, 3180-3183.
https://doi.org/10.1103/physrevlett.82.3180
Identifiers
- DOI
- 10.1103/physrevlett.82.3180