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Dynamics-sensitive centrality

Source: R/centrality-batch15.R
centrality_dynamics_sensitive.Rd

Liu et al.'s finite-time dynamics-sensitive (DS) centrality is \(S(T)=\sum_{r=0}^{T-1}\beta A[\beta A+(1-\mu)I]^r\mathbf{1}\), where beta is the spreading rate and mu the recovery rate (equation 5 in the preprint). This is the full recovery-parameter family. For mu=1, it reduces to \(\sum_{t=1}^{T}(\beta A)^t\mathbf{1}\) (equation 7), also the form listed in the Centrality Zoo. For mu=0 it gives the paper's susceptible-infected case.

Usage

centrality_dynamics_sensitive(x, ds_beta = 0.1, ds_mu = 1, ds_steps = 5, ...)

Arguments

x

Network input accepted by centrality.

ds_beta

Finite spreading rate between 0 and 1, default 0.1.

ds_mu

Finite recovery rate between 0 and 1, default 1.

ds_steps

Nonnegative integer horizon, default 5. Must not exceed .Machine$integer.max.

...

Additional arguments to centrality. With normalized = TRUE, positive scores are divided by their maximum.

Value

Named numeric vector in input node order.

Details

Uses the simple undirected unweighted skeleton, as in the source: either direction creates an edge, parallel edges count once and loops are removed. The projection of other inputs is an explicit cograph convention. mode, edge weights and shortest-path weight inversion do not affect this measure. Isolates score zero. T=0 or beta=0 returns zero; T=1 gives beta times degree. The initial seed itself is not added to the score.

This linearized cumulative spreading score allows repeated walks and can exceed the number of nodes. It is not a bounded infection probability or an exact simulation of the nonlinear SIR/SI process. Defaults beta=0.1, mu=1 and T=5 select a parameter setting studied in the paper; they are not fitted to the input network. Any finite horizon is supported without a spectral convergence condition, subject to numerical precision. Overflow raises an error, even if normalization is requested.

References

Liu, J. G., Lin, J. H., Guo, Q., & Zhou, T. (2016). Locating influential nodes via dynamics-sensitive centrality. Scientific Reports, 6, 21380. doi:10.1038/srep21380 . Preprint equations 5 and 7: https://arxiv.org/abs/1504.06672.

See also

centrality_diffusion_centrality.

Examples

g <- igraph::make_ring(5)
centrality_dynamics_sensitive(g, ds_beta = 0.1, ds_mu = 1, ds_steps = 5)
#>       1       2       3       4       5 
#> 0.24992 0.24992 0.24992 0.24992 0.24992 
centrality_dynamics_sensitive(g, ds_mu = 0)
#>       1       2       3       4       5 
#> 1.48832 1.48832 1.48832 1.48832 1.48832