Topological Coefficient

The topological coefficient (Stelzl et al. 2005) measures how far a node shares neighbors with the nodes it is linked to through a common neighbor: $$T(v) = \frac{\sum_{u \in U_v} J(v, u)}{|U_v|\, k_v},$$ where $U_v$ is the set of nodes that share at least one neighbor with $v$, $J(v, u)$ is the number of shared neighbors plus one when $u$ and $v$ are linked, and $k_v$ is the degree.

Usage

centrality_topological_coefficient(x, ...)

Arguments

x: Network input accepted by centrality.
...: Further arguments to centrality.

Value

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

Details

Edge weights and direction are ignored. A node that shares no neighbor with any other node scores 0, as does an isolated node. On undirected networks the values equal centiserve::topocoefficient().

References

Stelzl, U., Worm, U., Lalowski, M., Haenig, C., Brembeck, F. H., Goehler, H., et al. (2005). A human protein-protein interaction network: A resource for annotating the proteome. Cell, 122(6), 957-968. doi:10.1016/j.cell.2005.08.029 .

Examples

centrality_topological_coefficient(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>  0.6111111  0.6031746  0.6250000  0.6296296  0.5740741  0.7111111  0.7500000 
#>   Evaluate     Create      Share 
#>  0.7555556  0.6666667  0.7037037