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第2行： − − − − − + − In graph theory and network analysis, indicators of centrality identify the most important vertices within a graph. Applications include identifying the most influential person(s) in a social network, key infrastructure nodes in the Internet or urban networks, and super-spreaders of disease. Centrality concepts were first developed in social network analysis, and many of the terms used to measure centrality reflect their sociological origin.+ − − 在图论和网络分析中，中心性指标识别出一个图中最重要的顶点。用于识别社会网络中最有影响力的人、互联网或城市网络中的基础设施关键节点以及疾病的超级传播者。中心性概念最初在社会网络分析中发展起来，用来衡量中心性的许多术语反映了它们的社会学起源。 − − 它们（中心性）不应与节点影响度相混淆，后者意在量化网络中每个节点的影响。+ − − − + − ==中心性指标的定义与特性==
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{{for|the statistical concept|Central tendency}}
{{for|the statistical concept|Central tendency}}
{{Network Science}}
{{Network Science}}
In [[graph theory]] and [[network theory|network analysis]], indicators of '''centrality''' identify the most important [[vertex (graph theory)|vertices]] within a graph. Applications include identifying the most influential person(s) in a [[social network]], key infrastructure nodes in the [[Internet]] or [[urban network]]s, and [[super-spreader]]s of disease. Centrality concepts were first developed in [[social network analysis]], and many of the terms used to measure centrality reflect their [[sociology|sociological]] origin.<ref name="NewmanNetworks">Newman, M.E.J. 2010. ''Networks: An Introduction.'' Oxford, UK: Oxford University Press.</ref>
In [[graph theory]] and [[network theory|network analysis]], indicators of '''centrality''' identify the most important [[vertex (graph theory)|vertices]] within a graph. Applications include identifying the most influential person(s) in a [[social network]], key infrastructure nodes in the [[Internet]] or [[urban network]]s, and [[super-spreader]]s of disease. Centrality concepts were first developed in [[social network analysis]], and many of the terms used to measure centrality reflect their [[sociology|sociological]] origin.<ref name="NewmanNetworks">Newman, M.E.J. 2010. ''Networks: An Introduction.'' Oxford, UK: Oxford University Press.</ref>
In graph theory and network analysis, indicators of centrality identify the most important vertices within a graph. Applications include identifying the most influential person(s) in a social network, key infrastructure nodes in the Internet or urban networks, and super-spreaders of disease. Centrality concepts were first developed in , and many of the terms used to measure centrality reflect their sociological origin.
在'''<font color="#ff8000">图论 graph theory </font>'''和'''<font color="#ff8000">网络分析 network analysis </font>'''中，'''<font color="#ff8000">中心性 centrality </font>'''指标用于识别图中最重要的顶点。其应用包括在社会网络中识别出最有影响力的个人，在因特网或城市网络中识别出最为关键的基础设施节点，以及识别疾病的超级传播者。中心性的概念最初由'''<font color="#ff8000">社会网络分析 social network analysis</font>'''所发展，因此许多用于衡量中心性的术语都反映出了它们的社会学出身。
They should not be confused with [[node influence metric]]s, which seek to quantify the influence of every node in the network.
They should not be confused with [[node influence metric]]s, which seek to quantify the influence of every node in the network.
They should not be confused with node influence metrics, which seek to quantify the influence of every node in the network.
They should not be confused with node influence metrics, which seek to quantify the influence of every node in the network.
中心性不应与节点影响度相混淆，后者意在量化网络中每个节点的影响。
==Definition and characterization of centrality indices==
==中心性指标的定义与特性Definition and characterization of centrality indices==
Centrality indices are answers to the question "What characterizes an important vertex?" The answer is given in terms of a real-valued function on the vertices of a graph, where the values produced are expected to provide a ranking which identifies the most important nodes.<ref name="Bonacich1987">{{cite journal |last1= Bonacich |first1= Phillip|year= 1987 |title= Power and Centrality: A Family of Measures | journal=American Journal of Sociology |volume= 92|issue= 5|pages= 1170–1182|doi=10.1086/228631 |url= }}<!--|accessdate=July 11, 2014--></ref><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}}<!--|accessdate= July 11, 2014--></ref><ref name="Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista. 2018 E12201--E12208">{{cite journal |
Centrality indices are answers to the question "What characterizes an important vertex?" The answer is given in terms of a real-valued function on the vertices of a graph, where the values produced are expected to provide a ranking which identifies the most important nodes.<ref name="Bonacich1987">{{cite journal |last1= Bonacich |first1= Phillip|year= 1987 |title= Power and Centrality: A Family of Measures | journal=American Journal of Sociology |volume= 92|issue= 5|pages= 1170–1182|doi=10.1086/228631 |url= }}<!--|accessdate=July 11, 2014--></ref><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}}<!--|accessdate= July 11, 2014--></ref><ref name="Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista. 2018 E12201--E12208">{{cite journal |