# centr_eigen

From igraph v1.0.0
by Gabor Csardi

##### Centralize a graph according to the eigenvector centrality of vertices

See `centralize`

for a summary of graph centralization.

##### Usage

```
centr_eigen(graph, directed = FALSE, scale = TRUE,
options = arpack_defaults, normalized = TRUE)
```

##### Arguments

- graph
- The input graph.
- directed
- logical scalar, whether to use directed shortest paths for calculating eigenvector centrality.
- scale
- Whether to rescale the eigenvector centrality scores, such that the maximum score is one.
- options
- This is passed to
`eigen_centrality`

, the options for the ARPACK eigensolver. - normalized
- Logical scalar. Whether to normalize the graph level centrality score by dividing by the theoretical maximum.

##### Value

- A named list with the following components:
vector The node-level centrality scores. value The corresponding eigenvalue. options ARPACK options, see the return value of `eigen_centrality`

for details.centralization The graph level centrality index. theoretical_max The same as above, the theoretical maximum centralization score for a graph with the same number of vertices.

##### See Also

Other centralization related: `centr_betw_tmax`

,
`centralization.betweenness.tmax`

;
`centr_betw`

,
`centralization.betweenness`

;
`centr_clo_tmax`

,
`centralization.closeness.tmax`

;
`centr_clo`

,
`centralization.closeness`

;
`centr_degree_tmax`

,
`centralization.degree.tmax`

;
`centr_degree`

,
`centralization.degree`

;
`centr_eigen_tmax`

,
`centralization.evcent.tmax`

;
`centralization`

, `centralize`

,
`centralize.scores`

##### Examples

```
# A BA graph is quite centralized
g <- sample_pa(1000, m = 4)
centr_degree(g)$centralization
centr_clo(g, mode = "all")$centralization
centr_betw(g, directed = FALSE)$centralization
centr_eigen(g, directed = FALSE)$centralization
# The most centralized graph according to eigenvector centrality
g0 <- make_graph(c(2,1), n = 10, dir = FALSE)
g1 <- make_star(10, mode = "undirected")
centr_eigen(g0)$centralization
centr_eigen(g1)$centralization
```

*Documentation reproduced from package igraph, version 1.0.0, License: GPL (>= 2)*

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