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本词条由Ryan初步翻译

本词条由Ryan初步翻译

{{redirect|Network hub|the Ethernet technology|Ethernet hub}}

{{redirect|Network hub|the Ethernet technology|Ethernet hub}}

In network science, a hub is a node with a number of links that greatly exceeds the average. Emergence of hubs is a consequence of a scale-free property of networks. While hubs cannot be observed in a random network, they are expected to emerge in scale-free networks. The uprise of hubs in scale-free networks is associated with power-law distribution. Hubs have a significant impact on the network topology. Hubs can be found in many real networks, such as Brain Network or Internet.

In network science, a hub is a node with a number of links that greatly exceeds the average. Emergence of hubs is a consequence of a scale-free property of networks. While hubs cannot be observed in a random network, they are expected to emerge in scale-free networks. The uprise of hubs in scale-free networks is associated with power-law distribution. Hubs have a significant impact on the network topology. Hubs can be found in many real networks, such as Brain Network or Internet.

[[File:Network representation of brain connectivity.JPG|thumb|

[[File:Network representation of brain connectivity.JPG|thumb|

图1：Network representation of brain connectivity. Hubs are highlighted|150px|right] 表示大脑连接性的网络，其中枢纽节点被突出显示]

图1：Network representation of brain connectivity. Hubs are highlighted|150px|right] 表示大脑连接性的网络，其中枢纽节点被突出显示]

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.

一个枢纽节点是网络中具有高度值的一个组件。与网络中的其他节点相比，枢纽节点的链接数要大得多。无尺度网络中枢纽的链接数(度)远远高于随机网络中链接数最大的节点，在保持网络的大小''N''和平均度 ''<k>''不变的情况下。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，每个节点的度''k''是可比的，因此不可能出现枢纽节点。在无标度网络中，少数节点(即枢纽节点)具有高度值 ''k''，而其他节点只有少量的链接。

一个枢纽节点是网络中具有高度值的组件。与网络中的其他节点相比，枢纽节点的链接数要大得多。无尺度网络中枢纽的链接数(度)远远高于随机网络中链接数最大的节点，在保持网络的大小''N''和平均度 ''<k>''不变的情况下。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，每个节点的度''k''是可比的，因此不可能出现枢纽节点。在无标度网络中，少数节点(即枢纽节点)具有高度值 ''k''，而其他节点只有少量的链接。

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

枢纽节点的出现可以用无标度网络和随机网络的区别来解释。无标度网络(Barabási-Albert 模型)与随机网络(Erdős–Rényi 模型)在两个方面有所不同: (a)增长，(b)优先连接。{ Cite journal

枢纽节点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 Barabási-Albert model</font>'''与'''<font color="#ff8000">随机网络 Random Networks Erdős–Rényi model</font>'''在两个方面有所不同: (a)'''<font color="#ff8000">增长 Growth</font>'''，(b)'''<font color="#ff8000">优先连接 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

Emergence of hubs in networks is also related to time. In scale-free networks, nodes which emerged earlier have a higher chance of becoming a hub than latecomers. This phenomenon is called first-mover advantage and it explains why some nodes become hubs and some do not. However, in a real network, the time of emergence is not the only factor that influences the size of the hub. For example, Facebook emerged 8 years later after Google became the largest hub on the World Wide Web and yet in 2011 Facebook became the largest hub of WWW. Therefore, in real networks the growth and the size of a hub depends also on various attributes such as popularity, quality or the aging of a node.

Emergence of hubs in networks is also related to time. In scale-free networks, nodes which emerged earlier have a higher chance of becoming a hub than latecomers. This phenomenon is called first-mover advantage and it explains why some nodes become hubs and some do not. However, in a real network, the time of emergence is not the only factor that influences the size of the hub. For example, Facebook emerged 8 years later after Google became the largest hub on the World Wide Web and yet in 2011 Facebook became the largest hub of WWW. Therefore, in real networks the growth and the size of a hub depends also on various attributes such as popularity, quality or the aging of a node.

网络中枢纽节点的涌现也与时间有关。在无标度网络中，较早出现的节点比后来者更有可能成为枢纽。这种现象被称为先发优势，它解释了为什么一些节点成为枢纽，而一些没有。然而，在一个真实的网络中，出现的时间并不是影响枢纽规模的唯一因素。例如，在谷歌成为全球最大的互联网中心8年后，Facebook 出现了，然而在2011年，Facebook 成为了全球最大的互联网中心。因此，在实际网络中，枢纽的增长和规模也取决于各种属性，如节点的流行程度、质量或老化程度。

网络中枢纽节点的涌现也与时间有关。在无标度网络中，较早出现的节点比后来者更有可能成为枢纽。这种现象被称为'''<font color="#ff8000">先发优势 First-Mover Advantage</font>'''，它解释了为什么一些节点成为枢纽，而一些没有。然而，在一个真实的网络中，出现的时间并不是影响枢纽规模的唯一因素。例如，在谷歌成为全球最大的互联网中心8年后，Facebook 出现了，然而在2011年，Facebook 成为了全球最大的互联网中心。因此，在实际网络中，枢纽的增长和规模也取决于各种属性，如节点的流行程度、质量或老化程度。

=== Aging of hubs (nodes) 枢纽节点的老化===

=== '''<font color="#ff8000">枢纽节点的老化 Aging of hubs (nodes)</font>''' ===

The phenomenon present in real networks, when older hubs are shadowed in a network. This phenomenon is responsible for changes in evolution and topology of networks.<ref>[http://barabasi.com/networksciencebook/content/book_chapter_6.pdf Barabási, Albert-László. ''Network Science: Evolving Networks''., p. 3]</ref> The example of aging phenomenon may be the case of Facebook overtaking the position of the largest hub on the Web, Google(which was the largest node since 2000).{{Citation needed|date=May 2016}}

The phenomenon present in real networks, when older hubs are shadowed in a network. This phenomenon is responsible for changes in evolution and topology of networks.<ref>[http://barabasi.com/networksciencebook/content/book_chapter_6.pdf Barabási, Albert-László. ''Network Science: Evolving Networks''., p. 3]</ref> The example of aging phenomenon may be the case of Facebook overtaking the position of the largest hub on the Web, Google(which was the largest node since 2000).{{Citation needed|date=May 2016}}

The phenomenon present in real networks, when older hubs are shadowed in a network. This phenomenon is responsible for changes in evolution and topology of networks. The example of aging phenomenon may be the case of Facebook overtaking the position of the largest hub on the Web, Google(which was the largest node since 2000).

The phenomenon present in real networks, when older hubs are shadowed in a network. This phenomenon is responsible for changes in evolution and topology of networks. The example of aging phenomenon may be the case of Facebook overtaking the position of the largest hub on the Web, Google(which was the largest node since 2000).

这种现象在真实网络中出现，当旧的枢纽被隐藏在网络中时。这种现象导致了网络演化和拓扑结构的变化。老化现象的例子可参照 Facebook 超越了网络中最大的中心 Google (自2000年以来最大的节点)。

这种现象在真实网络中有所出现，当旧的枢纽被隐藏在网络中时。这种现象导致了网络演化和拓扑结构的变化。老化现象的例子可参照 Facebook 超越了网络中最大的中心 Google (自2000年以来最大的节点)。

=== Robustness and Attack Tolerance 鲁棒性和攻击容忍度===

=== '''<font color="#ff8000">鲁棒性和攻击容忍度 Robustness and Attack Tolerance</font>''' ===

During the random failure of nodes or targeted attack hubs are key components of the network. During the random failure of nodes in network hubs are responsible for exceptional robustness of network.<ref>{{cite journal|title=Resilience of the Internet to Random Breakdowns|

During the random failure of nodes or targeted attack hubs are key components of the network. During the random failure of nodes in network hubs are responsible for exceptional robustness of network.<ref>{{cite journal|title=Resilience of the Internet to Random Breakdowns|

During the random failure of nodes or targeted attack hubs are key components of the network. During the random failure of nodes in network hubs are responsible for exceptional robustness of network.<ref>{{cite journal|title=Resilience of the Internet to Random Breakdowns|

During the random failure of nodes or targeted attack hubs are key components of the network. During the random failure of nodes in network hubs are responsible for exceptional robustness of network.<ref>{{cite journal|title=Resilience of the Internet to Random Breakdowns|

随机故障的节点或定向攻击的枢纽是网络的关键组成部分。在网络中枢节点的随机失效过程中，网络的鲁棒性是由节点的随机失效决定的。< ref > { cite journal | title = Resilience of the Internet to Random breaks |  

随机故障的节点或定向攻击网络关键组成部分的枢纽。在网络枢纽节点的随机失效过程中，网络的鲁棒性是由节点的随机失效决定的。< ref > { cite journal | title = Resilience of the Internet to Random breaks |  

journal=Phys. Rev. Lett.|

journal=Phys. Rev. Lett.|

</ref> The chance that a random failure would delete the hub is very small, because hubs coexists with a large number of small degree nodes. The removal of small degree nodes does not have a large effect on integrity of network. Even though the random removal would hit the hub, the chance of fragmantation of network is very small because the remaining hubs would hold the network together. In this case, hubs are the strength of a scale-free networks.

</ref> The chance that a random failure would delete the hub is very small, because hubs coexists with a large number of small degree nodes. The removal of small degree nodes does not have a large effect on integrity of network. Even though the random removal would hit the hub, the chance of fragmantation of network is very small because the remaining hubs would hold the network together. In this case, hubs are the strength of a scale-free networks.

The perfect degree correlation means that each degree-k node is connected only to the same degree-k nodes. Such connectivity of nodes decide the topology of networks, which has an effect on robustness of network, the attribute discussed above. If the number of links between the hubs is the same as would be expected by chance, we refer to this network as Neutral Network. If hubs tend to connected to each other while avoiding linking to small-degree nodes we refer to this network as Assortative Network. This network is relatively resistant against attacks, because hubs form a core group, which is more reduntant against hub removal. If hubs avoid connecting to each other while linking to small-degree nodes, we refer to this network as Disassortative Network. This network has a hub-and-spoke character. Therefore, if we remove the hub in this type of network, it may damage or destroy the whole network.

The perfect degree correlation means that each degree-k node is connected only to the same degree-k nodes. Such connectivity of nodes decide the topology of networks, which has an effect on robustness of network, the attribute discussed above. If the number of links between the hubs is the same as would be expected by chance, we refer to this network as Neutral Network. If hubs tend to connected to each other while avoiding linking to small-degree nodes we refer to this network as Assortative Network. This network is relatively resistant against attacks, because hubs form a core group, which is more reduntant against hub removal. If hubs avoid connecting to each other while linking to small-degree nodes, we refer to this network as Disassortative Network. This network has a hub-and-spoke character. Therefore, if we remove the hub in this type of network, it may damage or destroy the whole network.

=== Spreading phenomenon ===

==='''<font color="#ff8000">传播效应 Spreading phenomenon</font>'''  ===

The hubs are also responsible for effective spreading of material on network. In an analysis of disease spreading or information flow, hubs are referred to as super-spreaders. Super-spreaders may have a positive impact, such as effective information flow, but also devastating in a case of epidemic spreading such as H1N1 or AIDS. The mathematical models such as model of H1H1 Epidemic prediction <ref>{{Cite journal|first1=Duygu |last1=Balcan |first2=Hao |last2=Hu |first3=Bruno |last3=Goncalves |first4=Paolo |last4=Bajardi |first5=Chiara |last5=Poletto |first6=Jose J.|last6=Ramasco|first7=Daniela|last7=Paolotti|first8=Nicola|last8=Perra |first9=Michele |last9=Tizzoni |first10=Wouter |last10=Van den Broeck|first11=Vittoria |last11=Colizza|first12=Alessandro |last12=Vespignani|date=14 September 2009|title=Seasonal transmission potential and activity peaks of the new influenza A(H1N1): a Monte Carlo likelihood analysis based on human mobility|journal=BMC Medicine |volume=7 |issue=45 |page=29 |doi=10.1186/1741-7015-7-45 |id= |pmid=19744314 |pmc=2755471 |arxiv=0909.2417}}</ref> may allow us to predict the spread of diseases based on human mobility networks, infectiousness, or social interactions among humans. Hubs are also important in the eradication of disease. In a scale-free network hubs are most likely to be infected, because of the large number of connections they have. After the hub is infected, it broadcasts the disease to the nodes it is linked to. Therefore, the selective immunization of hubs may be the cost-effective strategy in eradication of spreading disease.

The hubs are also responsible for effective spreading of material on network. In an analysis of disease spreading or information flow, hubs are referred to as super-spreaders. Super-spreaders may have a positive impact, such as effective information flow, but also devastating in a case of epidemic spreading such as H1N1 or AIDS. The mathematical models such as model of H1H1 Epidemic prediction <ref>{{Cite journal|first1=Duygu |last1=Balcan |first2=Hao |last2=Hu |first3=Bruno |last3=Goncalves |first4=Paolo |last4=Bajardi |first5=Chiara |last5=Poletto |first6=Jose J.|last6=Ramasco|first7=Daniela|last7=Paolotti|first8=Nicola|last8=Perra |first9=Michele |last9=Tizzoni |first10=Wouter |last10=Van den Broeck|first11=Vittoria |last11=Colizza|first12=Alessandro |last12=Vespignani|date=14 September 2009|title=Seasonal transmission potential and activity peaks of the new influenza A(H1N1): a Monte Carlo likelihood analysis based on human mobility|journal=BMC Medicine |volume=7 |issue=45 |page=29 |doi=10.1186/1741-7015-7-45 |id= |pmid=19744314 |pmc=2755471 |arxiv=0909.2417}}</ref> may allow us to predict the spread of diseases based on human mobility networks, infectiousness, or social interactions among humans. Hubs are also important in the eradication of disease. In a scale-free network hubs are most likely to be infected, because of the large number of connections they have. After the hub is infected, it broadcasts the disease to the nodes it is linked to. Therefore, the selective immunization of hubs may be the cost-effective strategy in eradication of spreading disease.