Extended mixed gravitational centrality

Extended mixed gravitational centrality (EMGC), also called IGC+, sums the raw MGC scores of immediate neighbors: \(EMGC_i=\sum_{j\in N(i)}MGC_j\). Each inner MGC score uses its own source node j's core number, partner degrees, and original-graph hop distances. The inner radius is centered on j, so a contribution can reach r+1 hops from i. Paths from j back to i are included. The outer neighbor sum has no distance or mass factor.

Usage

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

Arguments

x

Network input accepted by centrality.

gravity_radius

Nonnegative hop-distance cutoff, default three. NULL or infinity includes every reachable partner. Fractional cutoffs include exactly integer hop distances not exceeding them; values below one give zero. The optional "auto" is a cograph heuristic: round half the mean finite positive distance to the nearest integer (ties to even), with minimum one. It is not the cited radius rule and can change when disconnected components are added.

...

Additional arguments to centrality.

Value

Named numeric vector in input node order.

Details

Follows the reproduction in Li and Huang (2022), equation 8, attributed to Wang et al. (2018); the original full equations and software have not been inspected. Uses the same skeleton and radius conventions as centrality_mixed_gravity. Default inner radius three follows the reproduced definition; radius one matches the Zoo's literal inner neighbor sum. Optional maximum normalization occurs only after summing raw neighbor scores. Isolates and radii below one score zero. Empty and singleton graphs give no scores and zero, respectively. Dense O(n cubed) time and O(n squared) memory. Verification of these numerical equations does not establish author-software parity or predictive superiority.

References

Wang, J., Li, C. and Xia, C. (2018). doi:10.1016/j.amc.2018.04.028 . Definition read in Li, Z. and Huang, X. (2022), Scientific Reports, 12, 9879, equations 5-8 and reference 19. doi:10.1038/s41598-022-14005-3 .

Examples

centrality_extended_mixed_gravity(igraph::make_ring(6))
#>        1        2        3        4        5        6 
#> 20.88889 20.88889 20.88889 20.88889 20.88889 20.88889