# centr_eigen: Centralize a graph according to the eigenvector centrality of... In igraph: Network Analysis and Visualization

## Description

See `centralize` for a summary of graph centralization.

## Usage

 ```1 2 3 4 5 6 7``` ```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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```# 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 ```

### Example output

```Attaching package: 'igraph'

The following objects are masked from 'package:stats':

decompose, spectrum

The following object is masked from 'package:base':

union

 0.1623345
 0.4080763
 0.2183794
 0.938718
 1
 0.75
```

igraph documentation built on March 19, 2020, 5:13 p.m.