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删除1字节 、 2020年4月28日 (二) 15:41
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==<math>G(n,p)</math>的性质==
 
==<math>G(n,p)</math>的性质==
沿用上述符号,<math>G(n,p)</math>中的一个图平均有<math>\binom{n}{2}p</math>条连边。任意特定节点的度服从[https://en.wikipedia.org/wiki/Binomial_distribution 二项分布]:<ref>{{cite journal |last= Newman |first= Mark. E. J. |last2=Strogatz |first2=S. H. |last3=Watts |first3=D. J. |year= 2001 |title= Random graphs with arbitrary degree distributions and their applications|journal= Physical Review E|volume=64 |pages=026118|doi=[https://doi.org/10.1103/PhysRevE.64.026118 10.1103/PhysRevE.64.026118]|arxiv=[https://arxiv.org/abs/cond-mat/0007235 cond-mat/0007235]|bibcode=[http://adsabs.harvard.edu/abs/2001PhRvE..64b6118N 2001PhRvE..64b6118N]}}, Eq. (1)</ref>
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沿用上述符号,<math>G(n,p)</math>中的一个图平均有<math>\binom{n}{2}p</math>条连边。任意特定节点的度服从[https://en.wikipedia.org/wiki/Binomial_distribution 二项分布]:<ref>{{cite journal |last= Newman |first= Mark. E. J. |last2=Strogatz |first2=S. H. |last3=Watts |first3=D. J. |year= 2001 |title= Random graphs with arbitrary degree distributions and their applications|journal= Physical Review E|volume=64 |pages=026118|doi:[https://doi.org/10.1103/PhysRevE.64.026118 10.1103/PhysRevE.64.026118]|arxiv:[https://arxiv.org/abs/cond-mat/0007235 cond-mat/0007235]|bibcode:[http://adsabs.harvard.edu/abs/2001PhRvE..64b6118N 2001PhRvE..64b6118N]}}, Eq. (1)</ref>
:<math>P(\deg(v) = k) = {n-1\choose k}p^k(1-p)^{n-1-k},</math>
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:<math>P(\deg(v) = k) = {n-1\choose k}p^k(1-p)^{n-1-k},</math
 
其中n为图中节点的总数。由于
 
其中n为图中节点的总数。由于
 
:<math>P(\deg(v) = k) \to \frac{(np)^k \mathrm{e}^{-np}}{k!} \quad \text{ as } n \to \infty \text{ and } np = \text{ constant },</math>
 
:<math>P(\deg(v) = k) \to \frac{(np)^k \mathrm{e}^{-np}}{k!} \quad \text{ as } n \to \infty \text{ and } np = \text{ constant },</math>
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