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A hub is a component of a network with a high-degree node. Hubs have a significantly larger number of links in comparison with other nodes in the network. The number of links (degrees) for a hub in a scale-free network is much higher than for the biggest node in a random network, keeping the size N of the network and average degree <k> constant. The existence of hubs is the biggest difference between random networks and scale-free networks. In random networks, the degree k is comparable for every node; it is therefore not possible for hubs to emerge. In scale-free networks, a few nodes (hubs) have a high degree k while the other nodes have a small number of links.

A hub is a component of a network with a high-degree node. Hubs have a significantly larger number of links in comparison with other nodes in the network. The number of links (degrees) for a hub in a scale-free network is much higher than for the biggest node in a random network, keeping the size N of the network and average degree <k> constant. The existence of hubs is the biggest difference between random networks and scale-free networks. In random networks, the degree k is comparable for every node; it is therefore not possible for hubs to emerge. In scale-free networks, a few nodes (hubs) have a high degree k while the other nodes have a small number of links.

枢纽是拥有大度节点网络的重要构件。与网络中的其他节点相比，枢纽拥有的链接数量明显更多。在保持网络规模''N''和平均度 ''<k>''不变的情况下，无标度网络中枢纽拥有的链接数（度）远远高于随机网络中链接数最大的节点。枢纽的存在是随机网络和无标度网络的最大区别。在随机网络中，对于每个节点而言，度''k''是相当的，因此不可能出现枢纽节点。而在无标度网络中，少数节点(即枢纽)具有较高的度值 ''k''，而其他节点则只拥有少量的链接。

枢纽是拥有大度节点网络的重要构件。与网络中的其他节点相比，枢纽拥有的链接数量明显更多。在保持网络规模''N''和平均度 ''<k>''不变的情况下，无标度网络中枢纽拥有的链接数（度）远远高于随机网络中链接数最大的节点。枢纽的存在是随机网络和无标度网络的最大区别。在随机网络中，对于每个节点而言，度''k''是相当的，因此不可能出现枢纽节点。而在无标度网络中，少数节点（即枢纽）具有较高的度值 ''k''，而其他节点则只拥有少量的链接。

== Emergence 出现==

== Emergence 成因==

[[Image:Scale-free network sample.png|thumb|Example of a random network and a scale-free network|400px|right|

[[Image:Scale-free network sample.png|thumb|Example of a random network and a scale-free network|400px|right|

Emergence of hubs can be explained by the difference between scale-free networks and random networks. Scale-free networks (Barabási–Albert model) are different from random networks (Erdős–Rényi model) in two aspects: (a) growth, (b) preferential attachment.<ref name=RMP>{{Cite journal

Emergence of hubs can be explained by the difference between scale-free networks and random networks. Scale-free networks (Barabási–Albert model) are different from random networks (Erdős–Rényi model) in two aspects: (a) growth, (b) preferential attachment.<ref name=RMP>{{Cite journal

枢纽的出现可以用无标度网络和随机网络的区别来解释。'''<font color="#ff8000">无标度网络 Scale-Free Networks</font>'''（Barabási-Albert模型）与'''<font color="#ff8000">随机网络 Random Networks</font>'''（Erdős–Rényi model）的不同主要存在于如下两个方面: （a）'''<font color="#ff8000">增长 Growth</font>'''，（b）'''<font color="#ff8000">优先连接 Preferential Attachment</font>'''。{ Cite journal

枢纽的成因可以用无标度网络和随机网络的区别来解释。'''<font color="#ff8000">无标度网络 Scale-Free Networks</font>'''（Barabási-Albert模型）与'''<font color="#ff8000">随机网络 Random Networks</font>'''（Erdős–Rényi model）的区别主要存在于如下两个方面: （a）'''<font color="#ff8000">增长 Growth</font>'''，（b）'''<font color="#ff8000">优先链接 Preferential Attachment</font>'''。{ Cite journal

  | url = http://www.nd.edu/~networks/Publication%20Categories/03%20Journal%20Articles/Physics/StatisticalMechanics_Rev%20of%20Modern%20Physics%2074,%2047%20(2002).pdf

  | url = http://www.nd.edu/~networks/Publication%20Categories/03%20Journal%20Articles/Physics/StatisticalMechanics_Rev%20of%20Modern%20Physics%2074,%2047%20(2002).pdf

* (a) Scale-free networks assume a continuous growth of the number of nodes ''N'', compared to random networks which assume a fixed number of nodes. In scale-free networks the degree of the largest hub rises polynomially with the size of the network. Therefore, the degree of a hub can be high in a scale-free network. In random networks the degree of the largest node rises logaritmically (or slower) with N, thus the hub number will be small even in a very large network.

* (a) Scale-free networks assume a continuous growth of the number of nodes ''N'', compared to random networks which assume a fixed number of nodes. In scale-free networks the degree of the largest hub rises polynomially with the size of the network. Therefore, the degree of a hub can be high in a scale-free network. In random networks the degree of the largest node rises logaritmically (or slower) with N, thus the hub number will be small even in a very large network.

* (b) A new node in a scale-free network has a tendency to link to a node with a higher degree, compared to a new node in a random network which links itself to a random node. This process is called [[preferential attachment]]. The tendency of a new node to link to a node with a high degree ''k'' is characterized by [[Power law|power-law distribution]] (also known as rich-gets-richer process). This idea was introduced by [[Vilfredo Pareto]] and it explained why a small percentage of the population earns most of the money. This process is present in networks as well, for example 80 percent of web links point to 15 percent of webpages. The emergence of scale-free networks is not typical only of networks created by human action, but also of such networks as metabolic networks or illness networks.<ref>Barabási, Albert-László. ''Network Science: The Scale-Free Property''., p. 8.[http://barabasi.com/networksciencebook/content/book_chapter_2.pdf]</ref> This phenomenon may be explained by the example of hubs on the World Wide Web such as Facebook or Google. These webpages are very well known and therefore the tendency of other webpages pointing to them is much higher than linking to random small webpages.

* (b) A new node in a scale-free network has a tendency to link to a node with a higher degree, compared to a new node in a random network which links itself to a random node. This process is called [[preferential attachment]]. The tendency of a new node to link to a node with a high degree ''k'' is characterized by [[Power law|power-law distribution]] (also known as rich-gets-richer process). This idea was introduced by [[Vilfredo Pareto]] and it explained why a small percentage of the population earns most of the money. This process is present in networks as well, for example 80 percent of web links point to 15 percent of webpages. The emergence of scale-free networks is not typical only of networks created by human action, but also of such networks as metabolic networks or illness networks.<ref>Barabási, Albert-László. ''Network Science: The Scale-Free Property''., p. 8.[http://barabasi.com/networksciencebook/content/book_chapter_2.pdf]</ref> This phenomenon may be explained by the example of hubs on the World Wide Web such as Facebook or Google. These webpages are very well known and therefore the tendency of other webpages pointing to them is much higher than linking to random small webpages.

无标度网络中的新节点，与随机网络中的新节点相比，更倾向于连接到具有更高度的节点。这个过程称为优先依附。新节点连接到高度值''k''节点的趋势可被看做幂律分布(也被称作，越富有就越富有的过程)。这个想法是由Vilfredo Pareto提出的，它解释了为什么一小部分人赚了大部分的钱。这个过程也存在于网络中，例如80%的网络链接指向15%的网页。无标度网络的不仅是符合的人类活动网络，也可以拟合包括代谢网络或疾病网络。这种现象可以用像Facebook或谷歌这样的万维网中心的例子来解释。这些网页是非常有名的，因此其他网页指向他们的倾向比指向到随机的小网页要高得多。

*（b）无标度网络中的新节点倾向于链接到度较高的节点，而随机网络中的新节点则与其他节点随机相连。这一过程称为优先链接。新节点链接到度''k''较高节点的倾向可可以用幂律分布来刻画(即，富者越富)。这一想法由'''<font color="#ff8000">维尔弗雷多·帕累托 Vilfredo Pareto</font>'''提出，它解释了为什么一小部分人赚了大部分的钱。这个过程也存在于网络中，例如80%的网络链接指向15%的网页。无标度网络的出现并不仅仅是人类行为所创造的网络的典型现象，在新陈代谢网络或疾病网络中这一现象也十分常见。<ref>Barabási, Albert-László. ''Network Science: The Scale-Free Property''., p. 8.[http://barabasi.com/networksciencebook/content/book_chapter_2.pdf]</ref> 这种现象可以由像Facebook或谷歌这样的万维网枢纽的来解释。这些网页是非常有名的，因此相较于指向随机的小网页，其他网页指向他们的倾向要高得多。

The mathematical explanation for [[Barabási–Albert model]]:

The mathematical explanation for [[Barabási–Albert model]]:

The mathematical explanation for Barabási–Albert model:

The mathematical explanation for Barabási–Albert model:

Barabási-Albert 模型的数学解释:

Barabási-Albert模型的数学解释: