Node and Neighbor Layer Information Centrality

NINL (Zhu and Wang 2021) starts each node with the sum of the degrees $k_j$ in its closed neighborhood of radius $r$ and then, for $p$ iterations, replaces every score by the sum of the previous scores of its neighbors: $$NINL^{(p)} = A^p \, NINL^{(0)}, \qquad NINL^{(0)}_i = \sum_{j : d(i,j) \le r} k_j.$$

Usage

centrality_ninl(x, ninl_order = 3, ninl_radius = NULL, ...)

Arguments

x: Network input accepted by centrality.
ninl_order: Number of iterations $p$, a nonnegative integer. Default 3, as in the paper.
ninl_radius: Radius $r$. NULL (default) uses the automatic radius of the paper, a nonnegative integer fixes the hop radius, and Inf includes every reachable node.
...: Further arguments to centrality. The measure uses 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. The default radius is the ceiling of the average shortest-path length, as in the paper. On a disconnected network that average is infinite, so the default radius covers the whole component of each node. Isolated nodes score zero, and ninl_order = 0 returns the initial degree sums. With normalized = TRUE the scores are rescaled at every iteration, and on a bipartite network they can alternate between iterations. An invalid ninl_order or ninl_radius, and raw scores that overflow, raise an error.

References

Zhu, J. and Wang, L. (2021). Identifying Influential Nodes in Complex Networks Based on Node Itself and Neighbor Layer Information. Symmetry, 13, 1570. doi:10.3390/sym13091570 .

Examples

centrality_ninl(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>       7992       9828      11124       9504       7884       8046       6804 
#>   Evaluate     Create      Share 
#>       8586       9936       8640