MCGM (Li and Huang 2022) is a gravity model whose node mass combines degree \(K\), core number \(S\) and eigenvector centrality \(X\), each divided by its maximum over the network: $$MCGM_i = \sum_{j : 0 < d(i,j) \le R} \frac{m_i m_j}{d(i,j)^2}, \qquad m_i = K_i + \alpha S_i + X_i.$$ By default \(\alpha\) is the larger of the medians of \(K\) and \(X\) divided by the median of \(S\) (equation 17).
Arguments
- x
Network input accepted by
centrality.- mcgm_radius
Hop-distance cutoff \(R\). Default 2, the setting recommended in the paper.
NULLorInfincludes every reachable node.- mcgm_alpha
NULL(default) uses the median-based \(\alpha\). A finite nonnegative number replaces it.- ...
Further arguments to
centrality. The measure usesnormalized(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 and gravity_radius have no effect. On a
disconnected network the eigenvector feature is the projection of the
all-ones vector onto the dominant eigenspace, so a component with a
smaller spectral radius has \(X = 0\). When the median core
number is zero the automatic \(\alpha\) is undefined, and an
error asks for mcgm_alpha. mcgm_alpha = 1 gives equation
16 of the paper. Isolated nodes score zero, and an edgeless network or
a radius below one gives zero scores.
References
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 .