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==Freeman中心化==
 
==Freeman中心化==
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任何网络的中心化是一种对最中心的节点相对于其他中心节点如何更中心的度量。<ref name="Freeman1979">{{citation | journal = Social Networks | last1 = Freeman | first1 = Linton C. | year = 1979 | volume = 1 | issue = 3 | pages = 215–239 | title = centrality in social networks: Conceptual clarification | url = http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | doi = 10.1016/0378-8733(78)90021-7 | citeseerx = 10.1.1.227.9549 | access-date = 2014-07-31 | archive-url = https://web.archive.org/web/20160222033108/http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | archive-date = 2016-02-22 | url-status = dead }}</ref>中心化测量即:(a)计算所有节点与最中心节点的中心性之差的和;(b)将此和除以相同网络上理论情况下的最大值 。<ref name="Freeman1979">{{citation | journal = Social Networks | last1 = Freeman | first1 = Linton C. | year = 1979 | volume = 1 | issue = 3 | pages = 215–239 | title = centrality in social networks: Conceptual clarification | url = http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | doi = 10.1016/0378-8733(78)90021-7 | citeseerx = 10.1.1.227.9549 | access-date = 2014-07-31 | archive-url = https://web.archive.org/web/20160222033108/http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | archive-date = 2016-02-22 | url-status = dead }}</ref>因此,每一个中心性测量会有它自己的中心化度量。严格定义为, 如果,:<math>C_x(p_i)</math> 是点i的某种中心性测量,如果:<math>C_x(p_i)</math>是这种测量在这个网络上的最大值,同时如果,
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任何网络的中心化是一种对最中心的节点相对于其他中心节点如何更中心的度量。<ref name="Freeman1979">{{citation | journal = Social Networks | last1 = Freeman | first1 = Linton C. | year = 1979 | volume = 1 | issue = 3 | pages = 215–239 | title = centrality in social networks: Conceptual clarification | url = http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | doi = 10.1016/0378-8733(78)90021-7 | citeseerx = 10.1.1.227.9549 | access-date = 2014-07-31 | archive-url = https://web.archive.org/web/20160222033108/http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | archive-date = 2016-02-22 | url-status = dead }}</ref>中心化测量即:(a)计算所有节点与最中心节点的中心性之差的和;(b)将此和除以相同网络上理论情况下的最大值 。<ref name="Freeman1979">{{citation | journal = Social Networks | last1 = Freeman | first1 = Linton C. | year = 1979 | volume = 1 | issue = 3 | pages = 215–239 | title = centrality in social networks: Conceptual clarification | url = http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | doi = 10.1016/0378-8733(78)90021-7 | citeseerx = 10.1.1.227.9549 | access-date = 2014-07-31 | archive-url = https://web.archive.org/web/20160222033108/http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | archive-date = 2016-02-22 | url-status = dead }}</ref>因此,每一个中心性测量会有它自己的中心化度量。严格定义为, 如果<math>C_x(p_i)</math> 是点i的某种中心性测量,如果<math>C_x(p_i)</math>是这种测量在这个网络上的最大值,同时如果,
 
:<math>\max \sum _{{i=1}}^{{N}}C_{x}(p_{*})-C_{x}(p_{i})</math>
 
:<math>\max \sum _{{i=1}}^{{N}}C_{x}(p_{*})-C_{x}(p_{i})</math>
 
是所有点的中心性之差的和,任何有相同节点的图的<math>C_{x} </math>, 那么这个网络的中心化为:
 
是所有点的中心性之差的和,任何有相同节点的图的<math>C_{x} </math>, 那么这个网络的中心化为:
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