TY - JOUR

T1 - Scale-Free Networks Are Ultrasmall

AU - Cohen, Reuven

AU - Havlin, Shlomo

PY - 2003/2/7

Y1 - 2003/2/7

N2 - We study the diameter, or the mean distance between sites, in a scale-free network, having [Formula presented] sites and degree distribution [Formula presented], i.e., the probability of having [Formula presented] links outgoing from a site. In contrast to the diameter of regular random networks or small-world networks, which is known to be [Formula presented], we show, using analytical arguments, that scale-free networks with [Formula presented] have a much smaller diameter, behaving as [Formula presented]. For [Formula presented], our analysis yields [Formula presented], as obtained by Bollobas and Riordan, while for [Formula presented], [Formula presented]. We also show that, for any [Formula presented], one can construct a deterministic scale-free network with [Formula presented], which is the lowest possible diameter.

AB - We study the diameter, or the mean distance between sites, in a scale-free network, having [Formula presented] sites and degree distribution [Formula presented], i.e., the probability of having [Formula presented] links outgoing from a site. In contrast to the diameter of regular random networks or small-world networks, which is known to be [Formula presented], we show, using analytical arguments, that scale-free networks with [Formula presented] have a much smaller diameter, behaving as [Formula presented]. For [Formula presented], our analysis yields [Formula presented], as obtained by Bollobas and Riordan, while for [Formula presented], [Formula presented]. We also show that, for any [Formula presented], one can construct a deterministic scale-free network with [Formula presented], which is the lowest possible diameter.

UR - http://www.scopus.com/inward/record.url?scp=0037423295&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.90.058701

DO - 10.1103/PhysRevLett.90.058701

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C2 - 12633404

AN - SCOPUS:0037423295

SN - 0031-9007

VL - 90

SP - 4

JO - Physical Review Letters

JF - Physical Review Letters

IS - 5

ER -