Local Average Connectivity

Local average connectivity (Li et al. 2011) is the mean degree of the neighbors of a node within the subgraph $C_v$ induced by those neighbors: $$LAC(v) = \frac{1}{k_v} \sum_{u \in N(v)} k_u^{C_v},$$ where $k_u^{C_v}$ is the degree of $u$ inside $C_v$. High values mark nodes whose neighbors are tied to each other.

Usage

centrality_lac(x, mode = "all", ...)

Arguments

x: Network input accepted by centrality.
mode: Direction for directed networks: "all" (default), "out" or "in".
...: Further arguments to centrality.

Value

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

Details

Edge weights are ignored. mode selects the neighbors and the degree counted inside $C_v$. With mode = "all" on a directed network in-ties and out-ties are both counted, so a reciprocated tie counts twice. An isolated node scores 0.

References

Li, M., Wang, J., Chen, X., Wang, H., & Pan, Y. (2011). A local average connectivity-based method for identifying essential proteins from the network level. Computational Biology and Chemistry, 35(3), 143-150.

Examples

centrality_lac(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>   1.666667   2.285714   3.000000   1.666667   1.000000   2.000000   1.500000 
#>   Evaluate     Create      Share 
#>   2.400000   2.571429   2.333333