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Burt's Constraint

Source: R/centrality.R
centrality_constraint.Rd

Burt's constraint measures how much a node's ties are concentrated in contacts that are themselves tied to each other. With \(p_{ij}\) the proportion of the tie strength of \(i\) invested in \(j\), $$C_i = \sum_{j \ne i} \Big( p_{ij} + \sum_{q \ne i, j} p_{iq} p_{qj} \Big)^2.$$ Low constraint marks access to structural holes.

Usage

centrality_constraint(x, ...)

Arguments

x

Network input accepted by centrality.

...

Further arguments to centrality, such as normalized.

Value

A named numeric vector with one score per node, in input node order.

Details

Ties are symmetrized as \(w_{ij} + w_{ji}\) before the proportions are formed, so edge direction is ignored. With weighted = FALSE every tie has weight one. The values match igraph::constraint(). An isolated node returns NaN, and a node whose only tie is a self-loop scores 0.

See also

centrality_effective_size, centrality_bridging, centrality.

Examples

centrality_constraint(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>  0.3938089  0.3609471  0.4445897  0.2953747  0.3318307  0.3363414  0.4122426 
#>   Evaluate     Create      Share 
#>  0.3801232  0.4686083  0.3627823