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第1行： − 此词条暂由彩云小译翻译，正由Steve Luo整理和审校，带来阅读不便，请见谅。+ 第31行：
第31行： − + − − | author1 = Watts, D.J. − − 1 Watts，d.j. − − | author2 = Strogatz, S.H. − − | author2 = Strogatz, S.H. − − 2 Strogatz，s.h. − − | year = 1998 − − | year = 1998 − − 1998年 − − | title = Collective dynamics of 'small-world' networks − − | title = Collective dynamics of 'small-world' networks − − | 题目“小世界”网络的集体动态 − − | journal = Nature − − | journal = Nature − − 自然》杂志 − − | volume = 393 − − | volume = 393 − − 第393卷 − − | issue = 6684 − − | issue = 6684 − − 第6684期 − − | pages = 409–10 − − | pages = 409–10 − − 第409-10页 − − | doi = 10.1038/30918 − − | doi = 10.1038/30918 − − 10.1038 / 30918 − − | pmid = 9623998 − − | pmid = 9623998 − − 9623998 − − | bibcode=1998Natur.393..440W − − | bibcode=1998Natur.393..440W − − | bibcode 1998 / natur. 393. . 440 w − − }}</ref> − + − − ws { cite journal − + − − }}</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<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>。 + + 第118行：
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第55行： − 对于许多现实世界的网络来说，这个指数大约是3。然而，它不是一个通用常数，并且持续地依赖于网络的参数。+ − − − − 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 − − barabasi2000{ Cite journal − − | url = http://nd.edu/~networks/Publication%20Categories/03%20Journal%20Articles/Physics/Universality_Physical%20Rev%20Ltrs%2085,%205234%20(2000).pdf − − | url = http://nd.edu/~networks/Publication%20Categories/03%20Journal%20Articles/Physics/Universality_Physical%20Rev%20Ltrs%2085,%205234%20(2000).pdf − − Http://nd.edu/~networks/publication%20categories/03%20journal%20articles/physics/universality_physical%20rev%20ltrs%2085,%205234%20(2000).pdf − − | author1 = R. Albert − − | author1 = R. Albert − − 1 r. Albert − − | author2 = A.-L. Barabási − − | author2 = A.-L. Barabási − − | author2 A.-L. barab si − − | title = Topology of Evolving Networks: Local Events and Universality − − | title = Topology of Evolving Networks: Local Events and Universality − − 演化网络的拓扑结构: 局部事件与普适性 − − | journal = [[Physical Review Letters]] − − | journal = Physical Review Letters − − 物理评论快报 − − | volume = 85 − − | volume = 85 − − 第85卷 − − | issue = 24 − − | issue = 24 − − 第24期 − − | pages = 5234–5237 − − | pages = 5234–5237 − − 第5234-5237页 − − | year = 2000 − − | year = 2000 − − 2000年 − − | doi = 10.1103/PhysRevLett.85.5234 − | doi = 10.1103/PhysRevLett.85.5234+ − 10.1103 / physrvlett. 85.5234+ − − | pmid = 11102229 − − | pmid = 11102229 − − 11102229 − − − − − − − − }}</ref> − − }}</ref> − − {} / ref − − 第224行：
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第95行： + + − 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) − − 和 barab si a.-l. ，“复杂网络的统计力学” ，《现代物理学评论》74,47(2002) − − </ref> − − − − / 参考 − −
无编辑摘要
此词条暂由彩云小译翻译，已由Steve Luo审校。
[[Image:Barabasi Albert model.gif|thumb|256px|Animation of an evolving network according to the initial Barabasi–Albert model]]
[[Image:Barabasi Albert model.gif|thumb|256px|Animation of an evolving network according to the initial Barabasi–Albert model]]
瓦茨-斯托加茨图
瓦茨-斯托加茨图
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 | author1 = Watts, D.J.
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'''.
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 closures 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 closures 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
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模型无法像在现实世界网络中那样频繁地生成局部聚类和三元闭包。为此，提出了<font color="#ff8000">瓦茨-斯托加茨模型 Watts-Strogatz model</font>，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。
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模型无法像在现实世界网络中那样频繁地生成局部聚类和三元闭包。为此，提出了<font color="#ff8000">瓦茨-斯托加茨模型 Watts-Strogatz model</font>，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。<ref name=WS>{{cite journal | author1 = Watts, D.J. | author2 = Strogatz, S.H. | year = 1998 | title = Collective dynamics of 'small-world' networks | journal = Nature | volume = 393 | issue = 6684 | pages = 409–10 | doi = 10.1038/30918 | pmid = 9623998 | bibcode=1998Natur.393..440W}}</ref>
This produces a locally clustered network and dramatically reduces the [[average path length]], creating networks which represent the [[Small-world networks|small world phenomenon]] observed in many real world networks.<ref name=milg>{{cite journal |author1=Travers Jeffrey |author2=Milgram Stanley | year = 1969 | title = An Experimental Study of the Small World Problem | url = | journal = Sociometry | volume = 32 | issue = 4| pages = 425–443 | doi=10.2307/2786545|jstor=2786545 }}</ref>
This produces a locally clustered network and dramatically reduces the [[average path length]], creating networks which represent the [[Small-world networks|small world phenomenon]] observed in many real world networks.
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.
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>。<ref name=milg>{{cite journal |author1=Travers Jeffrey |author2=Milgram Stanley | year = 1969 | title = An Experimental Study of the Small World Problem | url = | journal = Sociometry | volume = 32 | issue = 4| pages = 425–443 | doi=10.2307/2786545|jstor=2786545 }}</ref>
Despite this achievement, both the ER and the Watts and Storgatz models fail to account for the formulation of hubs as observed in many real world networks. The degree distribution in the ER model follows a [[Poisson distribution]], while the Watts and Strogatz model produces graphs that are [[homogeneous]] in [[degree distribution|degree]]. Many networks are instead scale free, meaning that their degree distribution follows a [[power law]] of the form:
Despite this achievement, both the ER and the Watts and Storgatz models fail to account for the formulation of hubs as observed in many real world networks. The degree distribution in the ER model follows a [[Poisson distribution]], while the Watts and Strogatz model produces graphs that are [[homogeneous]] in [[degree distribution|degree]]. Many networks are instead scale free, meaning that their degree distribution follows a [[power law]] of the form:
尽管取得了这样的成就，ER模型和Watts-Storgatz模型都未能解释在许多现实世界网络中观察到的中心节点的形成。ER模型中的度分布遵循<font color="#ff8000">泊松分布</font>，而Watts-Strogatz模型生成的图在<font color="#ff8000">度</font>上是<font color="#ff8000">同质的</font>。但是，许多网络是无标度的，这意味着它们的度分布遵循以下形式的<font color="#ff8000">幂律分布</font>:
尽管取得了这样的成就，ER模型和Watts-Storgatz模型都未能解释在许多现实世界网络中观察到的中心节点的形成。ER模型中的度分布遵循<font color="#ff8000">泊松分布</font>，而Watts-Strogatz模型生成的图在<font color="#ff8000">度</font>上是<font color="#ff8000">同质的</font>。但是，许多网络是无标度的，这意味着它们的度分布遵循以下形式的<font color="#ff8000">幂律分布</font>:
: <math>P(k)\sim k^{-\gamma}</math>
: <math>P(k)\sim k^{-\gamma}</math>
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
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
对于许多现实世界的网络来说，这个指数大约是3。然而，它不是一个通用常数，并且持续地依赖于网络的参数。<ref name=Barabasi2000>{{Cite journal| url = http://nd.edu/~networks/Publication%20Categories/03%20Journal%20Articles/Physics/Universality_Physical%20Rev%20Ltrs%2085,%205234%20(2000).pdf | author1 = R. Albert | author2 = A.-L. Barabási | title = Topology of Evolving Networks: Local Events and Universality | journal = [[Physical Review Letters]] | volume = 85 | issue = 24 | pages = 5234–5237 | year = 2000 | doi = 10.1103/PhysRevLett.85.5234 | pmid = 11102229|arxiv = cond-mat/0005085 |bibcode = 2000PhRvL..85.5234A | hdl = 2047/d20000695 }}</ref>
|arxiv = cond-mat/0005085 |bibcode = 2000PhRvL..85.5234A | hdl = 2047/d20000695
|arxiv = cond-mat/0005085 |bibcode = 2000PhRvL..85.5234A | hdl = 2047/d20000695
| arxiv cond-mat / 0005085 | bibcode 2000PhRvL. . 85.5234 a | hdl 2047 / d20000695
==First evolving network model – scale-free networks 第一个演化网络模型——无标度网络==
==First evolving network model – scale-free networks 第一个演化网络模型——无标度网络==
{{Main| Barabási–Albert model }}
{{Main| Barabási–Albert model }}
The Barabási–Albert (BA) model was the first widely accepted model to produce [[scale-free network]]s. 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 network]]s. 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:
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:
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:
: <math>p_i = \frac{k_i}{\displaystyle\sum_j k_j},</math>
: <math>p_i = \frac{k_i}{\displaystyle\sum_j k_j},</math>
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。
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 适应度===
===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.
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.
与BA模型有关的一个问题是，每个节点的度分布经历很强的<font color="#ff8000">正反馈 positive feedback</font>，即最早的具有高度分布的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。<ref>Albert R. and Barabási A.-L., "Statistical mechanics of complex networks", ''Reviews of Modern Physics'' 74, 47 (2002)</ref>
与BA模型有关的一个问题是，每个节点的度分布经历很强的<font color="#ff8000">正反馈 positive feedback</font>，即最早的具有高度分布的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)
</ref>
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''.