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数学 p (k) sim k ^ {- gamma } / math

数学 p (k) sim k ^ {- gamma } / math

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

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<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:

巴拉巴西-阿尔伯特模型 Barabási–Albert model(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<font color="#ff8000">偏好依附 preferential attachment</font>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节点，而不是只有少量链接的节点。从形式上来说，这种偏好依附是:

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<font color="#ff8000">集聚系数 clustering coefficient</font>。

BA模型是第一个从随着时间的推移而添加节点和连边的网络构造方式中推导出网络拓扑的模型。然而，该模型只做了产生无标度网络所必需的最简单的假设，即存在线性增长和线性偏好依附。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.

One concern with the BA model is that the degree distributions of each nodes experience strong positive feedback whereby the earliest nodes with high degree distributions continue to dominate the network indefinitely. However, this can be alleviated by introducing a fitness for each node, which modifies the probability of new links being created with that node or even of links to that node being removed.<ref>

One concern with the BA model is that the degree distributions of each nodes experience strong positive feedback whereby the earliest nodes with high degree distributions continue to dominate the network indefinitely. However, this can be alleviated by introducing a fitness for each node, which modifies the probability of new links being created with that node or even of links to that node being removed.<ref>

Albert R. and Barabási A.-L., "Statistical mechanics of complex networks", ''Reviews of Modern Physics'' 74, 47 (2002)

Albert R. and Barabási A.-L., "Statistical mechanics of complex networks", ''Reviews of Modern Physics'' 74, 47 (2002)

In order to preserve the preferential attachment from the BA model, this fitness is then multiplied by the preferential attachment based on degree distribution to give the true probability that a link is created which connects to node i.

In order to preserve the preferential attachment from the BA model, this fitness is then multiplied by the preferential attachment based on degree distribution to give the true probability that a link is created which connects to node i.

为了保持 BA 模型中的优先链接，该适应度乘以基于度分布的优先链接，得到连接到节点 i 的真实概率。

为了保持BA模型中的优先链接，该适应度乘以基于度分布的优先链接，得到连接到节点 i 的真实概率。