Abstract
We study the diameter, or the mean distance between sites, in a scale-free network, having N sites and degree distribution p(k) proportional, variant k(-lambda), i.e., the probability of having k links outgoing from a site. In contrast to the diameter of regular random networks or small-world networks, which is known to be d approximately ln(N, we show, using analytical arguments, that scale-free networks with 2<lambda<3 have a much smaller diameter, behaving as d approximately ln(ln(N. For lambda=3, our analysis yields d approximately ln(N/ln(ln(N, as obtained by Bollobas and Riordan, while for lambda>3, d approximately ln(N. We also show that, for any lambda>2, one can construct a deterministic scale-free network with d approximately ln(ln(N, which is the lowest possible diameter.
Keywords
PhysicsLambdaCombinatoricsDegree (music)Quantum mechanicsMathematics
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Publication Info
- Year
- 2003
- Type
- article
- Volume
- 90
- Issue
- 5
- Pages
- 058701-058701
- Citations
- 799
- Access
- Closed
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Cite This
Reuven Cohen,
Shlomo Havlin
(2003).
Scale-Free Networks Are Ultrasmall.
Physical Review Letters
, 90
(5)
, 058701-058701.
https://doi.org/10.1103/physrevlett.90.058701
Identifiers
- DOI
- 10.1103/physrevlett.90.058701