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==Freeman centralization==

==Freeman centralization==

=='''<font color="#ff8000"> 弗里曼集中度Freeman centralization</font>'''==

=='''<font color="#ff8000"> 弗里曼中心度Freeman centralization</font>'''==

The '''centralization''' of any network is a measure of how central its most central node is in relation to how central all the other nodes are.<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> Centralization measures then (a) calculate the sum in differences in centrality between the most central node in a network and all other nodes; and (b) divide this quantity by the theoretically largest such sum of differences in any network of the same size.<ref name="Freeman1979"/>  Thus, every centrality measure can have its own centralization measure.  Defined formally, if <math>C_x(p_i)</math> is any centrality measure of point <math>i</math>, if <math>C_x(p_*)</math> is the largest such measure in the network, and if:

The '''centralization''' of any network is a measure of how central its most central node is in relation to how central all the other nodes are.<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> Centralization measures then (a) calculate the sum in differences in centrality between the most central node in a network and all other nodes; and (b) divide this quantity by the theoretically largest such sum of differences in any network of the same size.<ref name="Freeman1979"/>  Thus, every centrality measure can have its own centralization measure.  Defined formally, if <math>C_x(p_i)</math> is any centrality measure of point <math>i</math>, if <math>C_x(p_*)</math> is the largest such measure in the network, and if:

The centralization of any network is a measure of how central its most central node is in relation to how central all the other nodes are. Centralization measures then (a) calculate the sum in differences in centrality between the most central node in a network and all other nodes; and (b) divide this quantity by the theoretically largest such sum of differences in any network of the same size.  Thus, every centrality measure can have its own centralization measure.  Defined formally, if <math>C_x(p_i)</math> is any centrality measure of point <math>i</math>, if <math>C_x(p_*)</math> is the largest such measure in the network, and if:

The centralization of any network is a measure of how central its most central node is in relation to how central all the other nodes are. Centralization measures then (a) calculate the sum in differences in centrality between the most central node in a network and all other nodes; and (b) divide this quantity by the theoretically largest such sum of differences in any network of the same size.  Thus, every centrality measure can have its own centralization measure.  Defined formally, if <math>C_x(p_i)</math> is any centrality measure of point <math>i</math>, if <math>C_x(p_*)</math> is the largest such measure in the network, and if:

任何网络的集中度都是衡量其最核心的节点相对于其他所有节点的集聚程度的标准。<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>集中度的度量方法是: (a)计算网络中最中心的节点与所有其他节点之间的中心性差异之和; (b)将这个数量除以理论上相同规模的任何网络中这种差异之和的最大值。<ref name="Freeman1979"/>因此，每个中心性度量都可以有自己的集中度度量。正式定义，如果 < math > c _ x (p _ i) </math > 是点 < math > i </math > 的中心性度量，如果 < math > c _ x (p _ *) </math > 是网络中最大的中心性度量，如果:

任何网络的中心度都是衡量其最核心的节点相对于其他所有节点的集聚程度的标准。<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>中心度的度量方法是: (a)计算网络中最中心的节点与所有其他节点之间的中心性差异之和; (b)将这个数量除以理论上相同规模的任何网络中这种差异之和的最大值。<ref name="Freeman1979"/>因此，每个中心性度量都可以有自己的中心度度量。正式定义，如果 < math > c _ x (p _ i) </math > 是点 < math > i </math > 的中心性度量，如果 < math > c _ x (p _ *) </math > 是网络中最大的中心性度量，如果:

is the largest sum of differences in point centrality <math>C_x</math> for any graph with the same number of nodes, then the centralization of the network is:

is the largest sum of differences in point centrality <math>C_x</math> for any graph with the same number of nodes, then the centralization of the network is: