Dynamics-Sensitive Centrality

Dynamics-sensitive centrality (Liu et al. 2016) is a linearized cumulative spreading score with spreading rate $\beta$ and recovery rate $\mu$ over $T$ steps: $$S(T) = \sum_{r=0}^{T-1} \beta A \left[\beta A + (1-\mu) I\right]^r \mathbf{1}.$$ With $\mu = 1$ it reduces to $\sum_{t=1}^{T} (\beta A)^t \mathbf{1}$, the form listed in the Centrality Zoo, and $\mu = 0$ gives the 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: Spreading rate $\beta$, between 0 and 1. Default 0.1.
ds_mu: Recovery rate $\mu$, between 0 and 1. Default 1.
ds_steps: Horizon $T$, a nonnegative integer. Default 5.
...: Further arguments to centrality, such as normalized.

Value

A named numeric vector with one score per node, in input node order.

Details

The measure uses the simple undirected skeleton, so direction, weights, loops and parallel edges are ignored. Isolated nodes score 0. $T = 0$ or $\beta = 0$ gives 0, and $T = 1$ gives $\beta$ times the degree. The score counts repeated walks and can exceed the number of nodes, so it is not an infection probability. The defaults $\beta = 0.1$, $\mu = 1$ and $T = 5$ are one setting studied by Liu et al. (2016). Parameters outside their ranges raise an error.

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 .

Examples

centrality_dynamics_sensitive(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>    1.04422    1.25513    1.45154    1.23364    1.02868    1.05799    0.87553 
#>   Evaluate     Create      Share 
#>    1.09697    1.26998    1.09844