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===节点中心性===
===节点中心性===
Centrality indices produce rankings which seek to identify the most important nodes in a network model. Different centrality indices encode different contexts for the word "importance." The [[betweenness centrality]], for example, considers a node highly important if it form bridges between many other nodes. The [[Centrality#Eigenvector centrality|eigenvalue centrality]], in contrast, considers a node highly important if many other highly important nodes link to it. Hundreds of such measures have been proposed in the literature.
中心性指标可以给出所有节点的一个排序，用来寻找网络模型中最重要的节点。在不同的“重要性”的含义下，中心性指标也可以是不同的。例如[[介数中心性]]，在它定义下，如果一个节点和其他很多节点之间都有连接，那么它就是很重要的。而[[中心性#本征向量中心性|本征值中心性]]则相反，如果某个节点有很多很重要的节点和它相连，那么它就是很重要的。文献中给出了数百种这样的中心性的定义。
中心性指标可以给出所有节点的一个排序，用来寻找网络模型中最重要的节点。在不同的“重要性”的含义下，中心性指标也可以是不同的。例如[[介数中心性]]，在它定义下，如果一个节点和其他很多节点之间都有连接，那么它就是很重要的。而[[中心性#本征向量中心性|本征值中心性]]则相反，如果某个节点有很多很重要的节点和它相连，那么它就是很重要的。文献中给出了数百种这样的中心性的定义。
Centrality indices are only accurate for identifying the most central nodes. The measures are seldom, if ever, meaningful for the remainder of network nodes.
<ref name="Lawyer2015">
{{cite journal |last1= Lawyer |first1= Glenn |title= Understanding the spreading power of all nodes in a network| journal=Scientific Reports
|volume= 5 |pages= 8665 |date=March 2015
|number=O8665
| doi=10.1038/srep08665
|pmid= 25727453 |pmc= 4345333 |bibcode= 2015NatSR...5E8665L |arxiv=1405.6707}}
</ref>
<ref name="Sikic2013">
{{cite journal
|last1 = Sikic
|first1=Mile
|last2=Lancic
|first2=Alen
|last3= Antulov-Fantulin
|first3=Nino
|last4=Stefancic
|first4=Hrvoje
| title = Epidemic centrality -- is there an underestimated epidemic impact of network peripheral nodes?
| journal = European Physical Journal B
|date=October 2013
| volume = 86
| pages = 440
| number = 10
| doi=10.1140/epjb/e2013-31025-5
|arxiv=1110.2558
|bibcode=2013EPJB...86..440S
}}
</ref>
Also, their indications are only accurate within their assumed context for importance, and tend to "get it wrong" for other contexts.<ref name="Borgatti2005">
{{cite journal |last1= Borgatti |first1= Stephen P.|year= 2005 |title= Centrality and Network Flow |journal=Social Networks |volume= 27|issue= |pages= 55–71|doi=10.1016/j.socnet.2004.11.008 |url= |citeseerx= 10.1.1.387.419}}
</ref> For example, imagine two separate communities whose only link is an edge between the most junior member of each community. Since any transfer from one community to the other must go over this link, the two junior members will have high betweenness centrality. But, since they are junior, (presumably) they have few connections to the "important" nodes in their community, meaning their eigenvalue centrality would be quite low.
中心性指数只能准确地识别最重要的节点，这些测量很少(如果有的话)对其余的网络节点有意义。
中心性指数只能准确地识别最重要的节点，这些测量很少(如果有的话)对其余的网络节点有意义。
{{cite journal |last1= Borgatti |first1= Stephen P.|year= 2005 |title= Centrality and Network Flow |journal=Social Networks |volume= 27|issue= |pages= 55–71|doi=10.1016/j.socnet.2004.11.008 |url= |citeseerx= 10.1.1.387.419}}
{{cite journal |last1= Borgatti |first1= Stephen P.|year= 2005 |title= Centrality and Network Flow |journal=Social Networks |volume= 27|issue= |pages= 55–71|doi=10.1016/j.socnet.2004.11.008 |url= |citeseerx= 10.1.1.387.419}}
</ref> 例如，假设有两个互相分离的团块，只在两个团块中较小成员之间存在一条边。由于从一个团块到另外一个团块的任何迁移都要通过那一条边，因此这两个较小成员就会有很高的介数中心性。但是它们是重要性较低的成员，它们和“重要的”节点之间连接较少，这就意味着它们的本征值中心性较小。
</ref> 例如，假设有两个互相分离的团块，只在两个团块中较小成员之间存在一条边。由于从一个团块到另外一个团块的任何迁移都要通过那一条边，因此这两个较小成员就会有很高的介数中心性。但是它们是重要性较低的成员，它们和“重要的”节点之间连接较少，这就意味着它们的本征值中心性较小。
The concept of centrality in the context of static networks was extended, based on empirical and theoretical research, to dynamic centrality<ref name="dynamic1">{{cite journal | last1 = Braha | first1 = D. | last2 = Bar-Yam | first2 = Y. | year = 2006 | title = From Centrality to Temporary Fame: Dynamic Centrality in Complex Networks | url = | journal = Complexity | volume = 12 | issue = 2| pages = 59–63 | doi=10.1002/cplx.20156| arxiv = physics/0611295 | bibcode = 2006Cmplx..12b..59B }}</ref> in the context of time-dependent and temporal networks.<ref name="dynamic2">{{cite journal | last1 = Hill | first1 = S.A. | last2 = Braha | first2 = D. | year = 2010 | title = Dynamic Model of Time-Dependent Complex Networks | url = | journal = Physical Review E | volume = 82 | issue = 4| page = 046105 | doi=10.1103/physreve.82.046105| pmid = 21230343 | arxiv = 0901.4407 | bibcode = 2010PhRvE..82d6105H }}</ref><ref name="dynamic3">Gross, T. and Sayama, H. (Eds.). 2009. ''Adaptive Networks: Theory, Models and Applications.'' Springer.</ref><ref name="dynamic4">Holme, P. and Saramäki, J. 2013. ''Temporal Networks.'' Springer.</ref>
基于经验和理论的研究，静态网络上定义的中心性的概念可以拓展到时序网络中的动态中心性。<ref name="dynamic1">{{cite journal | last1 = Braha | first1 = D. | last2 = Bar-Yam | first2 = Y. | year = 2006 | title = From Centrality to Temporary Fame: Dynamic Centrality in Complex Networks | url = | journal = Complexity | volume = 12 | issue = 2| pages = 59–63 | doi=10.1002/cplx.20156| arxiv = physics/0611295 | bibcode = 2006Cmplx..12b..59B }}</ref><ref name="dynamic2">{{cite journal | last1 = Hill | first1 = S.A. | last2 = Braha | first2 = D. | year = 2010 | title = Dynamic Model of Time-Dependent Complex Networks | url = | journal = Physical Review E | volume = 82 | issue = 4| page = 046105 | doi=10.1103/physreve.82.046105| pmid = 21230343 | arxiv = 0901.4407 | bibcode = 2010PhRvE..82d6105H }}</ref><ref name="dynamic3">Gross, T. and Sayama, H. (Eds.). 2009. ''Adaptive Networks: Theory, Models and Applications.'' Springer.</ref><ref name="dynamic4">Holme, P. and Saramäki, J. 2013. ''Temporal Networks.'' Springer.</ref>
基于经验和理论的研究，静态网络上定义的中心性的概念可以拓展到时序网络中的动态中心性。<ref name="dynamic1">{{cite journal | last1 = Braha | first1 = D. | last2 = Bar-Yam | first2 = Y. | year = 2006 | title = From Centrality to Temporary Fame: Dynamic Centrality in Complex Networks | url = | journal = Complexity | volume = 12 | issue = 2| pages = 59–63 | doi=10.1002/cplx.20156| arxiv = physics/0611295 | bibcode = 2006Cmplx..12b..59B }}</ref><ref name="dynamic2">{{cite journal | last1 = Hill | first1 = S.A. | last2 = Braha | first2 = D. | year = 2010 | title = Dynamic Model of Time-Dependent Complex Networks | url = | journal = Physical Review E | volume = 82 | issue = 4| page = 046105 | doi=10.1103/physreve.82.046105| pmid = 21230343 | arxiv = 0901.4407 | bibcode = 2010PhRvE..82d6105H }}</ref><ref name="dynamic3">Gross, T. and Sayama, H. (Eds.). 2009. ''Adaptive Networks: Theory, Models and Applications.'' Springer.</ref><ref name="dynamic4">Holme, P. and Saramäki, J. 2013. ''Temporal Networks.'' Springer.</ref>