# subgraph.centrality

0th

Percentile

##### Find subgraph centrality scores of network positions

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

Keywords
graphs
##### Usage
subgraph.centrality (graph, diag=FALSE)
##### 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.

##### Value

• A numeric vector, the subgraph centrality scores of the vertices.

##### concept

Subgraph centrality

##### References

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

evcent, page.rank

##### Aliases
• subgraph.centrality
##### Examples
g <- ba.game(100, m=4, dir=FALSE)
sc <- subgraph.centrality(g)
cor(degree(g), sc)
Documentation reproduced from package igraph, version 0.6.5-2, License: GPL (>= 2)

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