Malatya centrality — centrality

The static Malatya score of a node is the sum of its degree divided by each neighbor's degree: \(M(i)=\sum_{j\in N(i)}d_i/d_j\). Computes the score on the original graph. On nonisolated vertices it is exactly the reciprocal of centrality_bridging_coefficient; this relationship follows from their definitions, not rank correlation.

Usage

centrality_malatya(x, ...)

Arguments

x: Network input accepted by centrality.
...: 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: either direction creates an edge, parallel edges count once and self-loops are removed. This is an explicit projection of other inputs to the source's domain. The empty neighbor sum assigns isolates zero. On a regular graph the score equals degree. High scores favor nodes with many neighbors of low degree.

References

Karci, A., Yakut, S., & Oztemiz, F. (2022). A New Approach Based on Centrality Value in Solving the Minimum Vertex Cover Problem: Malatya Centrality Algorithm. Journal of Computer Science, 7(2), 81-88, equation 1. doi:10.53070/bbd.1195501 .

Examples

centrality_malatya(igraph::make_star(5, mode = "undirected"))
#>     1     2     3     4     5 
#> 16.00  0.25  0.25  0.25  0.25