Subgraph centrality of a vertex measures the number of subgraphs a vertex participates in, weighting them according to their size.

## Details

The subgraph centrality of a vertex is defined as the number of closed walks originating at the vertex, where longer walks are downweighted by the factorial of their length.

Currently the calculation is performed by explicitly calculating all eigenvalues and eigenvectors of the adjacency matrix of the graph. This effectively means that the measure can only be calculated for small graphs.

## References

Ernesto Estrada, Juan A. Rodriguez-Velazquez: Subgraph
centrality in Complex Networks. *Physical Review E* 71, 056103 (2005).

## See also

`eigen_centrality()`

, `page_rank()`

Centrality measures
`alpha_centrality()`

,
`authority_score()`

,
`betweenness()`

,
`closeness()`

,
`diversity()`

,
`eigen_centrality()`

,
`harmonic_centrality()`

,
`hits_scores()`

,
`page_rank()`

,
`power_centrality()`

,
`spectrum()`

,
`strength()`

## Author

Gabor Csardi csardi.gabor@gmail.com based on the Matlab code by Ernesto Estrada