Effective Size

Burt's effective size is the number of a node's contacts minus their redundancy, the average number of ties each contact has to the other contacts: $$ES(v) = k_v - \frac{1}{k_v} \sum_{j \in N(v)} |N(v) \cap N(j)|.$$ On an undirected network this is \(k_v - 2 t_v / k_v\), with \(t_v\) the number of ties among the contacts.

Usage

centrality_effective_size(x, ...)

Arguments

x

Network input accepted by centrality.

...

Further arguments to centrality, such as directed and normalized.

Value

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

Details

Edge weights are ignored. On a directed network each reciprocated neighbor enters the neighbor list twice, so \(k_v\) counts it twice and the result differs from that of the undirected skeleton. An isolated node scores 0.

See also

centrality_constraint, centrality_redundancy, centrality.

Examples

centrality_effective_size(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>   4.166667   4.714286   4.875000   4.333333   4.833333   3.400000   2.500000 
#>   Evaluate     Create      Share 
#>   3.000000   4.285714   3.666667