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→Freeman centralization
==Freeman centralization==
==Freeman centralization==
弗里曼中心度
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。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。因此，每个中心性度量都可以有自己的集中性度量。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:
<math>C_x=\frac{\sum_{i=1}^{N} C_x(p_*)-C_x(p_i)}{\max \sum_{i=1}^{N} C_x(p_*)-C_x(p_i)}.</math>
<math>C_x=\frac{\sum_{i=1}^{N} C_x(p_*)-C_x(p_i)}{\max \sum_{i=1}^{N} C_x(p_*)-C_x(p_i)}.</math>
< math > c _ x = frac { sum _ { i = 1} ^ { n } c _ x (p _ *)-c _ x (p _ i)}{ max sum _ { i = 1 ^ { n } c _ x (p _ *)-c _ x (p _ i)} . </math >
< math > c _ x = frac { sum _ { i = 1} ^ { n } c _ x (p _ *)-c _ x (p _ i)}{ max sum _ { i = 1 ^ { n } c _ x (p _ *)-c _ x (p _ i)} . </math >
== Dissimilarity based centrality measures ==
== Dissimilarity based centrality measures ==