Mixed gravitational centrality (Wang, Li and Xia 2018), also called improved gravitational centrality, uses the core number \(k_s(i)\) of the focal node and the degree \(k(j)\) of each partner node as masses: $$MGC_i = k_s(i) \sum_{j : 0 < d(i,j) \le r} \frac{k(j)}{d(i,j)^2}.$$
Arguments
- x
Network input accepted by
centrality.- gravity_radius
Hop-distance cutoff \(r\). Default 3.
NULLorInfincludes every reachable node, and a value below one gives zero scores.- ...
Further arguments to
centrality, such asnormalized(divide by the maximum, defaultFALSE).
Details
The measure is computed on the simple undirected skeleton of the
network, so direction, weights, loops and parallel edges are ignored,
and gravity_mass has no effect. The implementation follows the
reproduction of the method in Li and Huang (2022), equations 5-8. The
Centrality Zoo writes the inner sum over immediate neighbors, which
corresponds to gravity_radius = 1. Isolated nodes score zero, and
unreachable nodes contribute nothing. gravity_radius = "auto" is
a cograph heuristic that rounds half the mean finite distance to the
nearest integer, with a minimum of one. A negative radius raises an
error.
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 .