Resistance Curvature

The node resistance curvature of Devriendt and Lambiotte (2022) is $$p_i = 1 - \frac{1}{2} \sum_{j \sim i} w_{ij} R_{ij},$$ where the weights $w_{ij}$ are conductances and $R_{ij}$ is the effective resistance. It equals one minus half the expected degree of the node in a random spanning tree of its component.

Usage

centrality_resistance_curvature(x, ...)

Arguments

x: Network input accepted by centrality.
...: Further arguments to centrality. The measure uses weighted (default TRUE) and normalized (default FALSE), which divides by the largest score and leaves negative scores negative.

Value

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

Details

Edge weights are conductances, and weighted = FALSE uses the simple undirected skeleton. On a weighted directed network the two arcs between a pair are added. Self-loops are removed, mode has no effect, and negative or non-finite weights raise an error. Scores can be negative at tree-like junctions. On a tree the score is one minus half the degree, on an unweighted cycle or complete graph of $n$ nodes it is $1/n$, and an isolated node scores 1. The raw scores sum to the number of components.

References

Devriendt, K., & Lambiotte, R. (2022). Discrete curvature on graphs from the effective resistance. Journal of Physics: Complexity, 3, 025008. doi:10.1088/2632-072X/ac730d .

Examples

centrality_resistance_curvature(regulation_net)
#>     Explore        Plan     Monitor       Adapt     Reflect     Discuss 
#>  0.14703607  0.01598811  0.03846915 -0.01385168  0.04645520  0.10397189 
#>  Synthesize    Evaluate      Create       Share 
#>  0.33242747  0.13041545  0.13930439  0.05978396