Scale-free networks are ultrasmall.

@article{Cohen2003ScalefreeNA,
  title={Scale-free networks are ultrasmall.},
  author={R. Cohen and S. Havlin},
  journal={Physical review letters},
  year={2003},
  volume={90 5},
  pages={
          058701
        }
}
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… Expand

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References

SHOWING 1-10 OF 36 REFERENCES
疟原虫var基因转换速率变化导致抗原变异[英]/Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A
抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1(PfPMP1)与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用,在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员,通过启动转录不同的var基因变异体为抗原变异提供了分子基础。
Phys
  • Rev. E 63, 062101
  • 2001
Comb
  • Probab. Comput. 7, 295
  • 1998
Proc
  • Natl. Acad. Sci. U.S.A. 99, 15 879
  • 2002
cond-mat/0205476; see also R
  • Cohen, S. Havlin, and D. ben-Avraham, in Handbook of Graphs and Networks, edited by zS. Bornholdt and H. G. Schuster
  • 2002
Adv
  • Appl. Math. 26, 257
  • 2001
Adv. Appl. Math
  • Adv. Appl. Math
  • 2001
Nature (London) 411
  • 41
  • 2001
Phys
  • Rev. Lett. 87, 278701
  • 2001
Phys
  • Rev. E 64, 046135
  • 2001
...
1
2
3
4
...