Extended local bridging centrality — centrality_extended_local

Macker's two-hop localized bridging centrality multiplies betweenness of the focal node in its induced closed two-hop neighborhood by its bridging coefficient. Degrees for that coefficient come from the original graph. The ego network includes every edge between the selected vertices. Its shortest paths can be up to four edges long; this is not global betweenness with a path-length cutoff of two. Betweenness uses unordered pairs, excludes endpoints, and is not normalized by ego-network size.

Usage

centrality_extended_local_bridging(x, ...)

Arguments

x: Network input accepted by centrality.
...: Additional arguments to centrality. normalized = TRUE divides final scores by their maximum; all-zero scores remain zero. Ego betweenness is never scaled by ego size.

Value

Named numeric vector in input node order.

Details

Uses the same simple undirected unweighted projection and zero conventions as centrality_localized_bridging. Macker's separate weighted model uses link quality for degree and costs for paths; that model is outside this implementation. Native breadth-first path counts cost O(sum over ego networks of n_ego times (n_ego + m_ego)), at worst O(n to the fourth power), with O(n squared) memory. This measure is marked costly and must be selected explicitly or through include.

References

Macker, J. P. (2016). An improved local bridging centrality model for distributed network analytics. MILCOM, pp. 600-605, sections IV-V, equation 5 and Table I. doi:10.1109/MILCOM.2016.7795393 .

Examples

centrality_extended_local_bridging(igraph::make_graph("Zachary"))
#>          1          2          3          4          5          6          7 
#>  2.0189267  0.9933652  3.3244479  0.6045079  0.1720430  1.7090909  1.7090909 
#>          8          9         10         11         12         13         14 
#>  0.0000000  9.5411745  1.4091711  0.1720430  0.0000000  0.0000000  9.1625292 
#>         15         16         17         18         19         20         21 
#>  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000 22.6422477  0.0000000 
#>         22         23         24         25         26         27         28 
#>  0.0000000  0.0000000  2.0092462  0.5185185  0.6507937  0.0000000  3.8618643 
#>         29         30         31         32         33         34 
#>  0.9704532  0.4382172  4.2075394  9.3565470  1.1317356  1.1801784