Small-World Networks: Evidence for a Crossover Picture

Marc Barthélémy, Luís A. Nunes Amaral
1999 Physical Review Letters  
Watts and Strogatz [Nature 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 ℓ between any two vertices of the network is
more » ... 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 ≪ 1) ∼ p^-τ with τ≈ 2/3.
doi:10.1103/physrevlett.82.3180 fatcat:iacru5punvapjaaqi4r3loxuy4