# 枢纽

## 涌现

• （a）无标度网络假设节点数量N保持持续的增长，而随机网络则假设节点数量是固定的。在无标度网络中，最大枢纽的度随着网络规模的增大，呈多项式地上升。因此，在无标度网络中，枢纽的度可以很高。而在随机网络中，最大节点的度随N的增大而呈对数式（或更慢）的上升。因此即使在一个非常大的随机网络中，枢纽的数量也会很小。

Barabási-Albert模型的数学解释:

$\displaystyle{ p_i = \frac{k_i}{\sum_j k_j}, }$

## 属性

### 缩短网络路径长度

$\displaystyle{ \ell\sim\frac{\ln N}{\ln \ln N}. }$

## 参考文献

1. Barabási, Albert-László. Network Science: Graph Theory., p. 27
2. Albert R, Barabási AL (2002). "Statistical mechanics of complex networks" (PDF). Reviews of Modern Physics. 74: 47–97. arXiv:cond-mat/0106096. Bibcode:2002RvMP...74...47A. doi:10.1103/RevModPhys.74.47.
3. Barabási, Albert-László. Network Science: The Scale-Free Property., p. 8.[1]
4. Barabási, Albert-László. Network Science: The Scale-Free Property., p. 23.[2]
5. Barabási, Albert-László. Network Science: Evolving Networks., p. 3
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