{smcl} {* *! version 1.0.0 22avr2016}{...} {title:Title} {p2colset 9 18 22 2}{...} {p2col :nwStrengthcent {hline 2} Calculates Freeman centralization index (1979) of the nodes strength } {p2colreset}{...} {title:Syntax} {p 8 17 2} {cmdab: nwStrengthcent} [{cmd:,} {opt DIRection()} ] {synoptset 25 tabbed}{...} {synopthdr} {synoptline} {synopt:{opt DIRection()}} Indicates the strength direction for directed networks (default: outward) {synoptline} {p2colreset}{...} {title:Description} {pstd} {cmd:nwStrengthcent()} returns the Freeman centralization index of the nodes strength. In a famous article, Freeman defines a centralization index that could be adapted for all centrality measures {it:C} Let {it:C_i*} be the maximum value of {it:C_i} of all nodes {it:i} in the network. The Freeman centralization index corresponds to: F_C= (sum_i [C_{i*}-C_i]) / ( max(sum_i [C_{i*}-C_i])) More precisely, for the Strength centralization, we rewrote the denominator as the maximum difference possible in strength for a graph with the same dimensions (number of nodes and total weights {it:W}). F_s= (sum_i [s_{i*}-s_i]) / ((W-min(s_i)) (n-1)) See: Freeman, L. C. (1978). Centrality in social networks conceptual clarification. Social networks, 1(3), 215-239. {title:Saved results} {pstd}{cmd: nwStrength} saves the following scalars in {cmd:r()}: {pstd} {synoptset 14 tabbed}{...} {p2col 5 14 18 2: }{p_end} {synopt:{cmd:r(s_central)}} Strength centralization index{p_end} {p2colreset}{...} {title:Examples} {cmd:. webnwuse klas12b, nwclear} {cmd:. nwkeep klas12b_wave2} {cmd:. nwStrengthcent,direction(outward)} {title:Author} Charlie Joyez, Paris-Dauphine University charlie.joyez@dauphine.fr {title:See also} {pstd} {cmd:nwStrengthcent} requires the {bf : nwcommands} package developed by Thomas Grund. {pstd} For do-files and ancillary files, see: {cmd:. net describe nwcommands-ado, from(http://www.nwcommands.org)} For help files, see : {cmd:. net describe nwcommands-hlp, from(http://www.nwcommands.org)}