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 ρ 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 ρ. We propose that the average distance (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*(ρ «K 1) - ρ~T with T ≈ 2/3.
|Original language||English (US)|
|Title of host publication||The Structure and Dynamics of Networks|
|Publisher||Princeton University Press|
|Number of pages||4|
|ISBN (Print)||0691113572, 9780691113579|
|State||Published - Oct 23 2011|
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