Improved Iterative Resource Allocation

Improved iterative resource allocation (Zhong, Liu and Shang 2015) is centrality_ira with the receiver's share scaled by its spreading capacity $1 - (1 - \beta)^{k_i}$, where $k_i$ is the degree and $\beta$ the spreading rate. The recursion $I(t+1) = A\,I(t)$ runs a fixed number of steps from $I(0) = (1, \dots, 1)$. $$a_{ij} = \left[1 - (1 - \beta)^{k_i}\right] \frac{\theta_i}{\sum_{u \in \Gamma(j)} \theta_u}$$

Usage

centrality_iira(
  x,
  ira_mass = "coreness",
  iira_beta = 0.2,
  iira_steps = 50,
  ...
)

Arguments

x: Network input accepted by centrality.
ira_mass: Node centrality $\theta$: "coreness" (default) or "degree".
iira_beta: Spreading rate $\beta$, a number in $(0, 1]$ (default 0.2).
iira_steps: Number of iterations, a nonnegative whole number (default 50).
...: Further arguments to centrality, such as normalized (divide by the maximum, default FALSE).

Value

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

Details

The measure is computed on the simple undirected skeleton of the network, so direction, weights, loops and parallel edges are ignored. Every column of $A$ sums to less than one, so the scores decay geometrically and only their order carries meaning. normalized = TRUE divides them by their maximum. Each connected component decays at its own rate, so raw scores are comparable only within a component, and a large iira_steps underflows to zero. An isolate scores zero, and iira_steps = 0 returns a vector of ones. The Centrality Zoo (section 2.185) states a different matrix, which is stochastic in neither direction and does not reproduce the source's worked example. The implementation follows the source.

References

Zhong, L.-F., Liu, J.-G. and Shang, M.-S. (2015). Iterative resource allocation based on propagation feature of node for identifying the influential nodes. Physics Letters A, 379(38), 2272-2276. doi:10.1016/j.physleta.2015.05.021 .

Examples

centrality_iira(regulation_net, normalized = TRUE)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>  0.6118850  0.8072822  1.0000000  0.7927596  0.6000654  0.6172813  0.4448479 
#>   Evaluate     Create      Share 
#>  0.6368730  0.8172584  0.6391343