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第21行： − 对网络的研究可以追溯到图论的发展，1736年 Leonhard Euler 首先分析了图论，当时他写了著名的柯尼斯堡七桥问题。概率网络理论是在八篇著名的随机图研究论文的基础上发展起来的。Erd s-r nyi 模型(ER)假定一个图由 n 个标记节点组成，其中每一对节点通过一个预设的概率 p 连接。+ 第29行：
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第131行： − 对于许多现实世界的网络来说，这个指数大约是3，然而，它不是一个通用常数，并且连续地依赖于网络的参数，例如 barabasi2000{ Cite journal+ 第210行：
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→Network theory background 网络理论背景
The study of networks traces its foundations to the development of graph theory, which was first analyzed by Leonhard Euler in 1736 when he wrote the famous Seven Bridges of Königsberg paper. Probabilistic network theory then developed with the help of eight famous papers studying random graphs written by Paul Erdős and Alfréd Rényi. The Erdős–Rényi model (ER) supposes that a graph is composed of N labeled nodes where each pair of nodes is connected by a preset probability p.
The study of networks traces its foundations to the development of graph theory, which was first analyzed by Leonhard Euler in 1736 when he wrote the famous Seven Bridges of Königsberg paper. Probabilistic network theory then developed with the help of eight famous papers studying random graphs written by Paul Erdős and Alfréd Rényi. The Erdős–Rényi model (ER) supposes that a graph is composed of N labeled nodes where each pair of nodes is connected by a preset probability p.
网络科学的研究可以追溯至图论的发展，1736年 Leonhard Euler 首先分析了图论，当时他写下了著名的柯尼斯堡七桥问题。随后概率网络理论在 Paul Erdős 和 Alfréd Rényi 的八篇著名的随机图研究论文的基础上发展起来。Erdős–Rényi 模型(ER模型)假定一个图由 n 个有标记的节点组成，其中每一对节点通过一个预设的概率 p 连接。
Watts–Strogatz graph
Watts–Strogatz graph
瓦茨-斯托加茨曲线图
瓦茨-斯托加茨图
While the ER model's simplicity has helped it find many applications, it does not accurately describe many real world networks. The ER model fails to generate local clustering and [[triadic closure]]s as often as they are found in real world networks. Therefore, the [[Watts and Strogatz model]] was proposed, whereby a network is constructed as a regular ring lattice, and then nodes are rewired according to some probability '''β'''.<ref name=WS>{{cite journal
While the ER model's simplicity has helped it find many applications, it does not accurately describe many real world networks. The ER model fails to generate local clustering and [[triadic closure]]s as often as they are found in real world networks. Therefore, the [[Watts and Strogatz model]] was proposed, whereby a network is constructed as a regular ring lattice, and then nodes are rewired according to some probability '''β'''.<ref name=WS>{{cite journal
While the ER model's simplicity has helped it find many applications, it does not accurately describe many real world networks. The ER model fails to generate local clustering and triadic closures as often as they are found in real world networks. Therefore, the Watts and Strogatz model was proposed, whereby a network is constructed as a regular ring lattice, and then nodes are rewired according to some probability β.<ref name=WS>{{cite journal
While the ER model's simplicity has helped it find many applications, it does not accurately describe many real world networks. The ER model fails to generate local clustering and triadic closures as often as they are found in real world networks. Therefore, the Watts and Strogatz model was proposed, whereby a network is constructed as a regular ring lattice, and then nodes are rewired according to some probability β.<ref name=WS>{{cite journal
尽管 ER 模型的简单性帮助它找到了许多应用程序，但它并不能准确地描述许多真实世界的网络。Er 模型不能像现实网络中常见的那样产生局部聚类和三元闭包。为此，提出了 Watts-Strogatz 模型，将网络构造成规则的环网格，然后根据一定的概率重新布线节点。 引用名称 ws { cite journal
尽管 ER 模型的简单性帮助它找到了许多应用之处，但它并不能准确地描述许多真实世界的网络。ER 模型不能产生现实网络中常见的局部聚类和三元闭包。为此提出了 Watts-Strogatz 模型，将网络构造成规则的环网格，然后根据一定的概率'''β'''重新连接节点。 引用名称 ws { cite journal
| author1 = Watts, D.J.
| author1 = Watts, D.J.
}}</ref> This produces a locally clustered network and dramatically reduces the average path length, creating networks which represent the small world phenomenon observed in many real world networks.
}}</ref> This produces a locally clustered network and dramatically reduces the average path length, creating networks which represent the small world phenomenon observed in many real world networks.
} / ref 这会产生一个局部聚集的网络，并显著减少平均路径长度，创建网络，代表在许多现实世界网络中观察到的小世界现象。
} / ref 这会产生一个局部聚集的网络，并显著减少平均路径长度。这样创建的网络可以代表在许多现实世界网络中观察到的小世界现象。
Despite this achievement, both the ER and the Watts and Storgatz models fail to account for the formulation of hubs as observed in many real world networks. The degree distribution in the ER model follows a Poisson distribution, while the Watts and Strogatz model produces graphs that are homogeneous in degree. Many networks are instead scale free, meaning that their degree distribution follows a power law of the form:
Despite this achievement, both the ER and the Watts and Storgatz models fail to account for the formulation of hubs as observed in many real world networks. The degree distribution in the ER model follows a Poisson distribution, while the Watts and Strogatz model produces graphs that are homogeneous in degree. Many networks are instead scale free, meaning that their degree distribution follows a power law of the form:
尽管取得了这样的成就，ER 模型、 Watts 模型和 Storgatz 模型都未能解释在许多现实世界网络中观察到的集线器的形成。模型中的度分布遵循泊松分佈，而 Watts 和 Strogatz 模型生成的图在度上是均匀的。许多网络是无标度的，这意味着它们的学位分布遵循一种形式的幂定律:
尽管取得了这样的成就，ER 模型、 Watts-Storgatz 模型都未能解释在许多现实世界网络中观察到的中心节点的形成。ER模型中的度分布遵循泊松分佈，而 Watts-Strogatz 模型生成的图在度上是均匀的。许多网络是无标度的，这意味着它们的度分布遵循这种形式的幂律:
This exponent turns out to be approximately 3 for many real world networks, however, it is not a universal constant and depends continuously on the network's parameters <ref name=Barabasi2000>{{Cite journal
This exponent turns out to be approximately 3 for many real world networks, however, it is not a universal constant and depends continuously on the network's parameters <ref name=Barabasi2000>{{Cite journal
对于许多现实世界的网络来说，这个指数大约是3。然而，它不是一个通用常数，并且连续地依赖于网络的参数。 barabasi2000{ Cite journal
| url = http://nd.edu/~networks/Publication%20Categories/03%20Journal%20Articles/Physics/Universality_Physical%20Rev%20Ltrs%2085,%205234%20(2000).pdf
| url = http://nd.edu/~networks/Publication%20Categories/03%20Journal%20Articles/Physics/Universality_Physical%20Rev%20Ltrs%2085,%205234%20(2000).pdf
{} / ref
{} / ref
==First evolving network model – scale-free networks==
==First evolving network model – scale-free networks==