Diversity Centrality

Diversity centrality (Eagle, Macy and Claxton 2010) is the Shannon entropy of the weights on the edges incident to a node, divided by its maximum $\log_2 k_v$: $$D(v) = -\frac{\sum_{j} p_{vj} \log_2 p_{vj}}{\log_2 k_v}, \qquad p_{vj} = \frac{|w_{vj}|}{\sum_{l} |w_{vl}|}.$$ The score lies between 0 and 1 and reaches 1 when the weights are equal.

Usage

centrality_diversity(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

On a directed network incoming and outgoing edges are separate entries, and $k_v$ counts both. With weighted = FALSE, or on an unweighted input, every node with two or more edges scores 1. A node with fewer than two edges, or with edge weights summing to zero, scores 0.

References

Eagle, N., Macy, M., & Claxton, R. (2010). Network diversity and economic development. Science, 328(5981), 1029-1031. doi:10.1126/science.1186605 .

Examples

centrality_diversity(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>  0.9320667  0.9361137  0.9217224  0.9643772  0.8742906  0.9697116  0.8368385 
#>   Evaluate     Create      Share 
#>  0.9262201  0.9582511  0.9748653