Mixed gravitational centrality (MGC), also called improved gravitational centrality (IGC), uses the focal node's core number as its mass and the partner node's degree as its mass: \(MGC_i=k_s(i)\sum_{j:0<d(i,j)\le r}k(j)/d(i,j)^2\). All degrees, core numbers and hop distances are measured on the original simple undirected graph. The masses are asymmetric even though distances are symmetric. This differs from using core numbers on both ends or degree on both ends of each interaction.
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.
Details
The implementation follows the explicit reproduction of Wang et al.'s
method in Li and Huang (2022), equations 5-8, with default radius three.
The original 2018 full equations and author software have not been
inspected. The Zoo summary writes an immediate-neighbor inner sum;
gravity_radius = 1 reproduces that literal interpretation.
Numerical verification establishes agreement with the cited reproduced
definition, not parity with unavailable original software or a guarantee
of spreading performance.
Uses the simple undirected unweighted skeleton: either arc creates an edge, parallel edges count once and loops are removed. This projection is a cograph convention outside the source domain. Edge weights, mode, cutoff, gravity_mass and path-weight inversion are ignored. Isolates and singleton graphs score zero; empty graphs return no scores. Unreachable partners contribute zero. With a fixed radius, adding a disconnected component leaves existing raw scores unchanged. Optional maximum normalization applies to the complete result over all nodes. Dense all-pairs distances cost O(n cubed) time and O(n squared) memory.
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 .
Definition read in Li, Z. and Huang, X. (2022). Identifying influential spreaders by gravity model considering multi-characteristics of nodes. Scientific Reports, 12, 9879. Equations 5-8 and reference 19. doi:10.1038/s41598-022-14005-3 .