KED Centrality

The KED method (Chen et al. 2014) combines a node's degree $k_i$ with the number and the diversity of the local paths that leave it. The local path number $K_i = \sum_{j \in N(i)} k_j$ is the neighbors' degree sum, and the path diversity $H_i$ is the entropy of the shares $p_j = k_j / K_i$ divided by $\log k_i$. $$KED_i = k_i \, (1 + H_i) \, \exp(K_i / N), \qquad H_i = \frac{-\sum_{j \in N(i)} p_j \log p_j}{\log k_i}$$

Usage

centrality_ked(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

The measure is computed on the simple undirected skeleton of the network, so direction, weights, loops and parallel edges are ignored. The source's directed variant is not implemented. $H_i$ lies in $[0, 1]$, and it is set to zero for a node with one neighbor, where it is $0/0$. Isolates score zero. $N$ is the number of nodes in the whole network, so adding a disconnected component changes every score and can change the ranking. The source's stated range $1 \le \exp(K_i/N) \le e$ holds only when $K_i \le N$, and an overflow of the exponential raises an error. The Centrality Zoo (section 2.215) adds exponents, drops the $1 +$ term and divides by the largest $K_l$. That form does not reproduce the scores printed in the source.

References

Chen, D.-B., Xiao, R., Zeng, A. and Zhang, Y.-C. (2014). Path diversity improves the identification of influential spreaders. Europhysics Letters, 104(6), 68006. doi:10.1209/0295-5075/104/68006 .

Examples

centrality_ked(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>   148.6091   293.1288   564.9522   265.3054   133.9247   164.2483    87.9635 
#>   Evaluate     Create      Share 
#>   200.5071   324.5153   200.5071