*! version 1.0.0 22avr2016

Title

nwStrengthcent -- Calculates Freeman centralization index (1979) of the nodes strength

Syntax

nwStrengthcent
[,
DIRection()
]

DIRection() Indicates the strength direction for directed networks (default: outward)

Description

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 C

Let C_i* be the maximum value of C_i of all nodes i in the network.
The Freeman centralization index corresponds to:
F_C= (sum_i [C_-C_i]) / ( max(sum_i [C_-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 W).

F_s= (sum_i [s_-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.

Saved results

nwStrength saves the following scalars in r():

r(s_central) Strength centralization index

Examples

. webnwuse klas12b, nwclear
. nwkeep klas12b_wave2
. nwStrengthcent,direction(outward)

Author

Charlie Joyez, Paris-Dauphine University
charlie.joyez@dauphine.fr

See also

nwStrengthcent requires the nwcommands package developed by Thomas Grund.

For do-files and ancillary files, see:

. net describe nwcommands-ado, from(http://www.nwcommands.org)

For help files, see :

. net describe nwcommands-hlp, from(http://www.nwcommands.org)