s-shell Index

The s-shell index (Liu, Tang, Do and Hui 2017) peels the network like the k-shell decomposition but by a strength computed from the topology. Each link gets the asymmetric weight $$w_{ij} = 1 + (k_i\, k^{out}_j)^a,$$ where $k^{out}_j$ counts the neighbors of $j$ outside the closed neighborhood of $i$, and the strength of $i$ is $s_i = \sum_{j \in N(i)} w_{ij}$. At each step the nodes at the minimum remaining strength are removed, the removals cascade, and the removed nodes receive the next shell index.

Usage

centrality_s_shell(x, s_shell_a = 0.5, ...)

Arguments

x: Network input accepted by centrality.
s_shell_a: Exponent $a$ of the link weights (default 0.5, the value the source recommends).
...: Further arguments to centrality.

Value

A named integer vector with one shell index per node, in input node order.

Details

Direction, edge weights and self-loops are ignored. The index is an ordinal counter starting at 1 for the outermost shell, so values are comparable within a network only. Higher indices mark more central nodes. Isolated nodes form shell 1 on their own and shift every other shell up by one. With $a = 0$ the shells are the dense ranks of the k-core numbers. A s_shell_a that is not a single non-negative number raises an error of class cograph_bad_parameter.

References

Liu, Y., Tang, M., Do, Y., & Hui, P. M. (2017). Accurate ranking of influential spreaders in networks based on dynamically asymmetric link weights. Physical Review E, 96(2), 022323.

Examples

centrality_s_shell(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>          2          2          2          2          2          2          1 
#>   Evaluate     Create      Share 
#>          2          2          2