Extended Mixed Gravitational Centrality

Extended mixed gravitational centrality (Wang, Li and Xia 2018), also called IGC+, sums the mixed gravitational scores of the immediate neighbors of a node: $$EMGC_i = \sum_{j \in N(i)} MGC_j.$$

Usage

centrality_extended_mixed_gravity(x, gravity_radius = 3, ...)

Arguments

x: Network input accepted by centrality.
gravity_radius: Hop-distance cutoff of the inner scores. Default 3. NULL or Inf includes every reachable node.
...: Further arguments to centrality, such as normalized (divide by the maximum, default FALSE).

Value

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

Details

Each inner score $MGC_j$ uses the radius around $j$, so a contribution can come from up to gravity_radius + 1 hops from the focal node. The implementation follows the reproduction in Li and Huang (2022), equation 8. The input handling and radius options of centrality_mixed_gravity apply, so direction, weights, loops and parallel edges are ignored. Isolated nodes score zero.

References

Wang, J., Li, C. and Xia, C. (2018). Improved centrality indicators to characterize the nodal spreading capability in complex networks. Applied Mathematics and Computation, 334, 388-400. doi:10.1016/j.amc.2018.04.028 .

Li, Z. and Huang, X. (2022). Identifying influential spreaders by gravity model considering multi-characteristics of nodes. Scientific Reports, 12, 9879. doi:10.1038/s41598-022-14005-3 .

Examples

centrality_extended_mixed_gravity(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>        687        838        959        821        682        689        570 
#>   Evaluate     Create      Share 
#>        717        843        720