Neighborhood Centrality

Neighborhood centrality (Liu et al. 2016) adds to a node's benchmark centrality $\theta$ the benchmark centrality of the endpoints of its non-backtracking walks of length 1 to $n$, discounted by $a^k$ at step $k$. With the defaults (degree benchmark, two steps, $a = 0.2$) it is the neighbor distance centrality. $$C_i = \theta_i + a \sum_{j \in \Gamma_i} \theta_j + a^2 \sum_{j \in \Gamma_i} \sum_{l \in \Gamma_j \setminus i} \theta_l + \dots$$

Usage

centrality_neighbor_distance(
  x,
  nd_order = 2,
  nd_decay = 0.2,
  nd_mass = "degree",
  ...
)

Arguments

x: Network input accepted by centrality.
nd_order: Number of steps $n$, a nonnegative whole number (default 2).
nd_decay: Per-step decay $a$, a finite number (default 0.2).
nd_mass: Benchmark centrality $\theta$: "degree" (default) or "coreness".
...: 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. Each level excludes only the node the walk came from, so a walk may revisit a node. Isolates score $\theta_i$, which is zero for both benchmarks, and nd_order = 0 returns the benchmark itself. The source takes $a$ in $[0, 1]$, and the function accepts any finite value. The Centrality Zoo paraphrases the measure with sums over distance shells, which agree with the source's walk sums on trees and differ on graphs with short cycles. The implementation follows the source.

References

Liu, Y., Tang, M., Zhou, T. and Do, Y. (2016). Identify influential spreaders in complex networks, the role of neighborhood. Physica A: Statistical Mechanics and its Applications, 452, 289-298. doi:10.1016/j.physa.2016.02.028 .

Examples

centrality_neighbor_distance(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>      15.32      18.24      20.68      17.80      15.04      15.56      13.20 
#>   Evaluate     Create      Share 
#>      16.36      18.52      16.40