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.
centrality_extended_mixed_gravity(x, gravity_radius = 3, ...)Named numeric vector in input node order.
Network input accepted by centrality.
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.
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.
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. tools:::Rd_expr_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. tools:::Rd_expr_doi("10.1038/s41598-022-14005-3").
centrality_extended_mixed_gravity(igraph::make_ring(6))
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