Subgraph Centrality

Subgraph centrality (Estrada and Rodriguez-Velazquez 2005) counts the closed walks that start and end at a node, weighting a walk of length \(k\) by \(1/k!\): $$SC(i) = \sum_{k=0}^{\infty} \frac{(A^k)_{ii}}{k!} = \left(e^{A}\right)_{ii}.$$

Usage

centrality_subgraph(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

\(A\) is the binary adjacency matrix without self-loops, so edge weights are ignored. On a directed network \(A\) is replaced by \(A + A^{T}\), so a reciprocated pair has entry 2; the values then equal igraph::subgraph_centrality(). An empty network raises an error.

References

Estrada, E., & Rodriguez-Velazquez, J. A. (2005). Subgraph centrality in complex networks. Physical Review E, 71(5), 056103. doi:10.1103/PhysRevE.71.056103 .

See also

centrality_communicability, centrality_eigenvector, centrality.

Examples

centrality_subgraph(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>   45.25014   64.11032   82.01339   42.15599   41.70540   34.34402   24.23952 
#>   Evaluate     Create      Share 
#>   38.64971   71.07596   57.03478