TY - JOUR
T1 - Small-world networks
T2 - Evidence for a crossover picture
AU - Barthélémy, Marc
AU - Nunes Amaral, Luis A.
PY - 1999
Y1 - 1999
N2 - 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 - 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 ≪ 1)˜p-τ with τ≈2/3.
AB - 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 - 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 ≪ 1)˜p-τ with τ≈2/3.
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U2 - 10.1103/PhysRevLett.82.3180
DO - 10.1103/PhysRevLett.82.3180
M3 - Article
AN - SCOPUS:0038740915
SN - 0031-9007
VL - 82
SP - 3180
EP - 3183
JO - Physical review letters
JF - Physical review letters
IS - 15
ER -