# R igraph manual pages

Use this if you are using igraph from R

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

### Description

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.

Other centralization related: `centr_betw_tmax`, `centr_betw`, `centr_clo_tmax`, `centr_clo`, `centr_degree_tmax`, `centr_degree`, `centr_eigen_tmax`, `centralize`

### 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
```

[Package igraph version 1.2.4 Index]