LineRank Centrality

LineRank (Kang et al. 2011) computes PageRank on the line graph, whose nodes are the edges of the network, and gives each node the sum of the stationary probabilities of its incident edges. In a directed network edge \(e\) leads to edge \(f\) when the target of \(e\) is the source of \(f\). In an undirected network two edges are adjacent when they share an endpoint (Kosa et al. 2015).

Usage

centrality_linerank(
  x,
  damping = 0.85,
  linerank_aggregation = "probability",
  ...
)

Arguments

x

Network input accepted by centrality.

damping

Probability of continuing the walk on the line graph, in \([0, 1)\). Default 0.85.

linerank_aggregation

"probability" (default) sums the stationary edge probabilities. "weight" multiplies them by the edge weights first.

...

Further arguments to centrality. The measure uses weighted (use edge weights, default TRUE) and normalized (divide by the maximum, default FALSE).

Value

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

Details

The walk on the line graph moves to an adjacent edge with probability proportional to that edge's weight and jumps to a uniformly chosen edge with probability 1 - damping. An edge without successors also jumps uniformly. With linerank_aggregation = "probability" the scores sum to two on a network with edges. With "weight" each stationary probability is multiplied by its edge weight before aggregation, following the weighted incidence matrix of Algorithm 2 in Kang et al. (2011). A loop contributes twice to its node, and an isolated node scores zero. Edge weights must be finite and nonnegative, and weighted = FALSE gives every edge weight one. A damping outside \([0, 1)\) raises an error.

References

Kang, U., Papadimitriou, S., Sun, J., & Tong, H. (2011). Centralities in Large Networks: Algorithms and Observations. Proceedings of the 2011 SIAM International Conference on Data Mining, 119-130. doi:10.1137/1.9781611972818.11 .

Kosa, B., Balassi, M., Englert, P., & Kiss, A. (2015). Betweenness versus Linerank. Computer Science and Information Systems, 12(1), 33-48. doi:10.2298/CSIS141101092K .

See also

centrality_pagerank, centrality_betweenness, centrality.

Examples

centrality_linerank(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#> 0.23711430 0.08083638 0.37402059 0.24709747 0.23941541 0.13042197 0.06670327 
#>   Evaluate     Create      Share 
#> 0.14344583 0.28715250 0.19379228