更改

数学，数学，数学

数学，数学，数学

==Additions to BA model==

==Additions to BA model= BA模型以外=

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]].  

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.  

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.

Therefore, the original model has since been modified to more fully capture the properties of evolving networks by introducing a few new properties.

Therefore, the original model has since been modified to more fully capture the properties of evolving networks by introducing a few new properties.

===Fitness===

===Fitness 适应度===

{{Main|Fitness model (network theory)}}

{{Main|Fitness model (network theory)}}

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 模型中的优先连接，该适应度乘以基于度分布的优先连接，得到连接到节点的连接的真实概率。

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。

Where <math>\eta</math> is the fitness, which may also depend on time. A decay of fitness with respect to time may occur and can be formalized by

Where <math>\eta</math> is the fitness, which may also depend on time. A decay of fitness with respect to time may occur and can be formalized by

where <math>\gamma</math> increases with <math>\nu.</math>

where <math>\gamma</math> increases with <math>\nu.</math>

数学 / 数学随着数学 / 数学的增长而增长-数学

其中<math>\gamma</math>随<math>\nu.</math>的增长而增长。

===Removing nodes and rewiring links===

===Removing nodes and rewiring links 删除节点和重连接边===

Further complications arise because nodes may be removed from the network with some probability. Additionally, existing links may be destroyed and new links between existing nodes may be created. The probability of these actions occurring may depend on time and may also be related to the node's fitness. Probabilities can be assigned to these events by studying the characteristics of the network in question in order to grow a model network with identical properties. This growth would take place with one of the following actions occurring at each time step:

Further complications arise because nodes may be removed from the network with some probability. Additionally, existing links may be destroyed and new links between existing nodes may be created. The probability of these actions occurring may depend on time and may also be related to the node's fitness. Probabilities can be assigned to these events by studying the characteristics of the network in question in order to grow a model network with identical properties. This growth would take place with one of the following actions occurring at each time step:

Further complications arise because nodes may be removed from the network with some probability. Additionally, existing links may be destroyed and new links between existing nodes may be created. The probability of these actions occurring may depend on time and may also be related to the node's fitness. Probabilities can be assigned to these events by studying the characteristics of the network in question in order to grow a model network with identical properties. This growth would take place with one of the following actions occurring at each time step:

Further complications arise because nodes may be removed from the network with some probability. Additionally, existing links may be destroyed and new links between existing nodes may be created. The probability of these actions occurring may depend on time and may also be related to the node's fitness. Probabilities can be assigned to these events by studying the characteristics of the network in question in order to grow a model network with identical properties. This growth would take place with one of the following actions occurring at each time step:

由于节点可能会以一定的概率从网络中移除，因此会出现更多的复杂情况。此外，现有的链接可能会被销毁，现有节点之间可能会创建新的链接。这些行为发生的概率可能取决于时间，也可能与节点的适应性有关。通过研究有关网络的特性，可以为这些事件赋予概率，从而生成具有相同特性的模型网络。这种增长将在每个时间步骤中发生下列行动之一:

由于节点可能会以一定的概率从网络中移除，因此会出现更多的复杂情况。此外，节点之间现有的链接可能会被删除并且创建新的链接。这些行为发生的概率可能取决于时间，也可能与节点的适应度有关。通过研究有关网络的特性，可以为这些事件赋予概率，从而生成具有相同特性的模型网络。这种增长将在每个时间步骤中发生下列行为之一:

Prob p: add an internal link.

Prob p: add an internal link.

Prob q: delete a link.

Prob q: delete a link.

问题: 删除链接。

概率 q: 删除一个链接。

Prob r: delete a node.

Prob r: delete a node.

Prob 1-p-q-r: add a node.

Prob 1-p-q-r: add a node.

Prob1-p-q-r: 添加一个节点。

概率 1-p-q-r: 添加一个节点。

 

 

==Other ways of characterizing evolving networks==

==Other ways of characterizing evolving networks==