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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 Barabasi-Albert 模型的网络演化动画

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

'''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.

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。

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。

}}</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。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。

} / ref 这会产生一个局部聚集的网络，并显著减少<font color="#ff8000">平均路径长度 average path length</font>。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<font color="#ff8000">小世界现象 small world phenomenon</font>。

The Barabási–Albert (BA) model was the first widely accepted model to produce scale-free networks. This was accomplished by incorporating preferential attachment and growth, where nodes are added to the network over time and are more likely to link to other nodes with high degree distributions. The BA model was first applied to degree distributions on the web, where both of these effects can be clearly seen. New web pages are added over time, and each new page is more likely to link to highly visible hubs like Google which have high degree distributions than to nodes with only a few links. Formally this preferential attachment is:

The Barabási–Albert (BA) model was the first widely accepted model to produce scale-free networks. This was accomplished by incorporating preferential attachment and growth, where nodes are added to the network over time and are more likely to link to other nodes with high degree distributions. The BA model was first applied to degree distributions on the web, where both of these effects can be clearly seen. New web pages are added over time, and each new page is more likely to link to highly visible hubs like Google which have high degree distributions than to nodes with only a few links. Formally this preferential attachment is:

Barabási–Albert (BA)模型是第一个被广泛接受的产生无标度网络的模型。这是通过合并优先链接和增长来实现的，随着时间的推移，节点被添加到网络中，并且更有可能链接到其他度较大的节点。BA 模型首先应用于互联网的度分布，这两种影响都可以清楚地看到。随着时间的推移，新的网页会不断增加，并且每个新的网页都更有可能链接到像谷歌这样具有很高的度分布的高度可见的中心，而不是只有少量链接的节点。从形式上来说，这种优先链接关系是:

Barabási–Albert (BA)模型是第一个被广泛接受的产生<font color="#ff8000">无标度网络 scale-free network</font>的模型。这是通过合并优先链接和增长来实现的，随着时间的推移，节点被添加到网络中，并且更有可能链接到其他度较大的节点。BA 模型首先应用于互联网的度分布，这两种影响都可以清楚地看到。随着时间的推移，新的网页会不断增加，并且每个新的网页都更有可能链接到像谷歌这样具有很高的度分布的高度可见的中心，而不是只有少量链接的节点。从形式上来说，这种优先链接关系是:

The BA model was the first model to derive the network topology from the way the network was constructed with nodes and links being added over time. However, the model makes only the simplest assumptions necessary for a scale-free network to emerge, namely that there is linear growth and linear preferential attachment. This minimal model does not capture variations in the shape of the degree distribution, variations in the degree exponent, or the size independent clustering coefficient.  

The BA model was the first model to derive the network topology from the way the network was constructed with nodes and links being added over time. However, the model makes only the simplest assumptions necessary for a scale-free network to emerge, namely that there is linear growth and linear preferential attachment. This minimal model does not capture variations in the shape of the degree distribution, variations in the degree exponent, or the size independent clustering coefficient.  

BA 模型是第一个随着时间依次增加节点和边来构建网络的模型。然而，这个模型只做了产生无标度网络必要的最简单的假设，即存在线性增长和线性优先链接。这个最小模型没有刻画度分布形状的变化，度指数的变化，或不依赖大小的集聚系数。

BA 模型是第一个随着时间依次增加节点和边来构建网络的模型。然而，这个模型只做了产生无标度网络必要的最简单的假设，即存在线性增长和线性优先链接。这个最小模型没有刻画度分布形状的变化，度指数的变化，或不依赖大小的<font color="#ff8000">集聚系数 clustering coefficient</font>。

Therefore, the original model has since been modified{{by whom?|date=June 2016}} to more fully capture the properties of evolving networks by introducing a few new properties.

Therefore, the original model has since been modified{{by whom?|date=June 2016}} to more fully capture the properties of evolving networks by introducing a few new properties.