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Animation of an evolving network according to the initial Barabasi–Albert model

Animation of an evolving network according to the initial Barabasi–Albert model

基于<font color="#ff8000">巴拉巴西-阿尔伯特 Barabasi-Albert </font>模型的网络演化动画

基于初始<font color="#ff8000">巴拉巴西-阿尔伯特 Barabasi-Albert </font>模型的演化网络的动画

'''Evolving networks''' are [[complex networks|networks]] that change as a function of time. They are a natural extension of [[network science]] since almost all real world networks evolve over time, either by adding or removing [[Vertex (graph theory)|nodes]] or links over time. Often all of these processes occur simultaneously, such as in [[social networks]] where people make and lose friends over time, thereby creating and destroying edges, and some people become part of new social networks or leave their networks, changing the nodes in the network. Evolving network concepts build on established [[network theory]] and are now being introduced into studying networks in many diverse fields.

'''Evolving networks''' are [[complex networks|networks]] that change as a function of time. They are a natural extension of [[network science]] since almost all real world networks evolve over time, either by adding or removing [[Vertex (graph theory)|nodes]] or links over time. Often all of these processes occur simultaneously, such as in [[social networks]] where people make and lose friends over time, thereby creating and destroying edges, and some people become part of new social networks or leave their networks, changing the nodes in the network. Evolving network concepts build on established [[network theory]] and are now being introduced into studying networks in many diverse fields.

Evolving networks are networks that change as a function of time. They are a natural extension of network science since almost all real world networks evolve over time, either by adding or removing nodes or links over time. Often all of these processes occur simultaneously, such as in social networks where people make and lose friends over time, thereby creating and destroying edges, and some people become part of new social networks or leave their networks, changing the nodes in the network. Evolving network concepts build on established network theory and are now being introduced into studying networks in many diverse fields.

Evolving networks are networks that change as a function of time. They are a natural extension of network science since almost all real world networks evolve over time, either by adding or removing nodes or links over time. Often all of these processes occur simultaneously, such as in social networks where people make and lose friends over time, thereby creating and destroying edges, and some people become part of new social networks or leave their networks, changing the nodes in the network. Evolving network concepts build on established network theory and are now being introduced into studying networks in many diverse fields.

<font color="#ff8000">演化网络 Evolving networks</font>是随着时间而变化的网络。它们是<font color="#ff8000">网络科学 network science</font>的自然延伸，因为几乎所有的现实世界的网络都是随着时间演化的，无论是通过随着时间的推移增加或删除节点或链接。通常所有这些过程都是同时发生的，比如在<font color="#ff8000">社交网络 social networks</font>中，随着时间的推移人们结交和失去朋友，从而创造和破坏边；一些人成为新的社交网络的一部分，或者离开他们的网络，从而改变网络中的节点。演化网络的概念建立在已有的网络理论基础之上，现在正被引入到许多不同领域的网络研究中。

<font color="#ff8000">演化网络 Evolving networks</font>是作为时间的函数而变化的网络。它们是<font color="#ff8000">网络科学 network science</font>的自然延伸，因为几乎所有现实世界的网络都是随时间演化的，通过随着时间的推移增加或删除节点或连边实现。通常所有这些过程都是同时发生的，比如在<font color="#ff8000">社交网络 social networks</font>中，随着时间的推移人们结交和失去朋友，从而创造和破坏连边，一些人成为新的社交网络的一部分，或者离开他们的网络，从而改变网络中的节点。演化网络的概念建立在既定的网络理论之上，现在正被引入到许多不同领域的网络研究中。

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<font color="#ff8000">图论 graph theory</font>的发展，1736年 Leonhard Euler 首先分析了图论，当时他写下了著名的<font color="#ff8000">柯尼斯堡七桥问题 Seven Bridges of Königsberg</font>。随后概率网络理论在 Paul Erdős 和 Alfréd Rényi 的八篇著名的<font color="#ff8000">随机图 random graphs</font>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。

网络研究源于<font color="#ff8000">图论 graph theory</font>的发展，莱昂哈德·欧拉 Leonhard Euler于1736年首先分析了图论，当时他撰写了著名的<font color="#ff8000">柯尼斯堡七桥问题 Seven Bridges of Königsberg</font>论文。随后在八篇由保罗·埃尔德什 Paul Erdős和阿尔弗雷德·雷尼 Alfréd Rényi撰写的研究<font color="#ff8000">随机图 random graphs</font>的著名论文的帮助下，概率网络理论得以发展。<font color="#ff8000">埃尔德什-雷尼模型 Erdős–Rényi model</font>(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。

瓦茨-斯托加茨图

瓦茨-斯托加茨图

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

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

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