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

## Arguments

- graph
The input graph, it should be undirected, but the implementation does not check this currently.

- diag
Boolean scalar, whether to include the diagonal of the adjacency matrix in the analysis. Giving

`FALSE`

here effectively eliminates the loops edges from the graph before the calculation.

## Details

The subgraph centrality of a vertex is defined as the number of closed loops originating at the vertex, where longer loops are exponentially downweighted.

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()`

,
`closeness()`

,
`diversity()`

,
`eigen_centrality()`

,
`estimate_betweenness()`

,
`harmonic_centrality()`

,
`hub_score()`

,
`page_rank()`

,
`power_centrality()`

,
`spectrum()`

,
`strength()`

## Author

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