320
个编辑
更改
跳到导航
跳到搜索
第233行：
第233行： − + 第239行：
第239行： − 英国广播公司模型是第一个根据网络的构建方式推导出网络拓扑广播模型的模型，随着时间的推移，网络中的节点和链路不断增加。然而，这个模型只做了最简单的假设，而这些假设对无尺度网络的出现是必要的，即存在线性增长和线性优先连接。这个最小模型没有捕捉度分布形状的变化，度指数的变化，或大小无关的集聚系数。+ 第245行：
第245行： − 因此，通过引入一些新的性质，对原有的模型进行了修改，以更充分地捕捉演化网络的性质。+ − + 第259行：
第259行： − Ba 模型的一个关注点是每个节点的度分布经历强正反馈，即最早的高度分布节点继续无限期地主宰网络。但是，可以通过为每个节点引入一个适应度来缓解这个问题，该适应度可以修改用该节点创建新链接的概率，甚至可以修改到该节点的链接被删除的概率。 裁判+ 第279行：
第279行： − + 第295行：
第295行： − 其中数学是适应性，这也可能取决于时间。适应性随时间的衰减可能会发生，并且可以通过+ 第311行：
第311行： − 数学 / 数学随着数学 / 数学的增长而增长-数学+ − + 第321行：
第321行： − 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:+ 第329行：
第329行： − 增加一个内部链接。+ 第337行：
第337行： − 问题: 删除链接。+ 第345行：
第345行： − 删除一个节点。+ 第353行：
第353行： − Prob1-p-q-r: 添加一个节点。+ − −
→Additions to BA model
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.
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。
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.
因此，通过引入一些新的性质，对原有的模型进行了修改，以更充分地刻画演化网络的性质。
===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>
BA 模型的一个关注点是每个节点的度分布经历很强的正反馈，即最早的高度分布节点继续无限期地主宰网络。但是，可以通过为每个节点引入一个适应度来缓解这个问题，该适应度可以修改用该节点创建新链接的概率，甚至可以修改该节点的链接被删除的概率。
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
其中<math>\eta</math>是适应度，这也可能依赖时间。适应度可能随时间衰减，可以表示为
where <math>\gamma</math> increases with <math>\nu.</math>
where <math>\gamma</math> increases with <math>\nu.</math>
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，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.
概率 p：增加一个内部链接。
Prob q: delete a link.
Prob q: delete a link.
概率 q: 删除一个链接。
Prob r: delete a node.
Prob r: delete a node.
概率 r：删除一个节点。
Prob 1-p-q-r: add a node.
Prob 1-p-q-r: add a node.
概率 1-p-q-r: 添加一个节点。
==Other ways of characterizing evolving networks==
==Other ways of characterizing evolving networks==