`nwevcent`

Eigenvector centrality

Syntax

nwevcent
[netname]
[,
generate(varname)
nosym
weighted
replace
binary]


`generate`(`varname`)	Required. Variable name for eigenvector centrality scores
`nosym`	do not symmetrize network before calculation
`weighted`	use the tie values of a valued network; redundant, this is the default (kept for compatibility)
`replace`	replace existing generate() variable
`binary`	Ignore the tie values of a valued network (by default they are used)

Description

Calculates eigenvector centrality for each node i in a netwwork and saves the result as a Stata variable. It assigns relative scores to all nodes in the network based on the concept that connections to high-scoring nodes contribute more to the score of the node in question than equal connections to low-scoring nodes.

By default, a valued network is dichotomized before calculation (any nonzero, non-missing tie value counts as a tie, regardless of magnitude) - the historical, still-default behavior of this command. Option weighted instead calculates on the tie values themselves, so that stronger ties contribute proportionally more, matching the standard weighted generalization of eigenvector centrality (Newman 2004, Bonacich power centrality). weighted has no effect on an unvalued network (there is nothing to weight by).

Eigenvector centrality is only defined for connected networks.

Examples

. nwwebuse gang, nwclear
. nwevcent gang, generate(_evcent)
. sum _evcent
. nwevcent gang, generate(_evcent_w) weighted

Supported network types

Binary: yes. Directed: yes - symmetrized by default (same “no-prefix trap” nosym convention as nwcloseness/nwkatz), nosym available. Weighted: not by default - weighted switches to the tie-value-weighted generalization (Newman 2004, Bonacich power centrality); has no effect on an unvalued network. Signed: not checked. Two-mode: same as for the bipartite graph read as a one-mode network (valid; no mode-specific normalisation).

References

Newman, M.E.J. (2004). Analysis of weighted networks. Physical Review E 70, 056131.

Bonacich, P. (1972). Factoring and weighting approaches to status scores and clique identification. Journal of Mathematical Sociology 2(1), 113-120.

nwevcent