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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>

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. |authorlink= |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 |issue= |pages=026118 |id= |url= |accessdate= |quote= |doi=10.1103/PhysRevE.64.026118|arxiv=cond-mat/0007235|bibcode=2001PhRvE..64b6118N |pmid= 11497662}}, Eq. (1)</ref>

:<math>P(\deg(v) = k) = {n-1\choose k}p^k(1-p)^{n-1-k},</math

:<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>