Improved Closeness Centrality

Improved closeness (Luan et al. 2021) divides each hop distance by a power of the number of shortest paths, so that a partner reached along many shortest paths counts as closer: $$ICC(i) = \frac{n-1}{\sum_{j \ne i} d_{ij} / \sigma_{ij}^{\alpha}}.$$ Here $d_{ij}$ is the hop distance and $\sigma_{ij}$ the number of shortest paths between $i$ and $j$.

Usage

centrality_improved_closeness(x, icc_alpha = 0.2, ...)

Arguments

x: Network input accepted by centrality.
icc_alpha: Exponent $\alpha$ of the number of shortest paths, between 0 and 1. Default 0.2, one of the values studied by Luan et al. (2021).
...: Further arguments to centrality, such as normalized.

Value

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

Details

The measure uses the simple undirected skeleton, so direction, weights, loops and parallel edges are ignored, and mode has no effect. With $\alpha = 0$ the score on a connected network is the normalized closeness, and on a tree it does not depend on $\alpha$. Scores can exceed 1. On a disconnected network every node scores 0, because each node has an unreachable partner at infinite distance. An isolated node also scores 0. A value of icc_alpha outside 0 to 1 raises an error.

References

Luan, Y., Bao, Z., & Zhang, H. (2021). Identifying Influential Spreaders in Complex Networks by Considering the Impact of the Number of Shortest Paths. Journal of Systems Science and Complexity, 34, 2168-2181. doi:10.1007/s11424-021-0111-7 .

Examples

centrality_improved_closeness(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>  0.7848073  0.8514053  0.8971799  0.8696763  0.8019894  0.8069843  0.7371681 
#>   Evaluate     Create      Share 
#>  0.8069843  0.8406205  0.7909990