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

 centr_eigen R Documentation

## 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
``````

igraph documentation built on Aug. 10, 2023, 9:08 a.m.