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==Freeman centralization==

==Freeman centralization==

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: