Measures of network centralisation

```
network_degree(object, normalized = TRUE, direction = c("all", "out", "in"))
network_closeness(object, normalized = TRUE, direction = c("all", "out", "in"))
network_betweenness(
object,
normalized = TRUE,
direction = c("all", "out", "in")
)
network_eigenvector(object, normalized = TRUE)
```

## Arguments

- object
An object of a migraph-consistent class:

matrix (adjacency or incidence) from `{base}`

R

edgelist, a data frame from `{base}`

R or tibble from `{tibble}`

igraph, from the `{igraph}`

package

network, from the `{network}`

package

tbl_graph, from the `{tidygraph}`

package

- normalized
Logical scalar, whether the centrality scores are normalized.
Different denominators are used depending on whether the object is one-mode or two-mode,
the type of centrality, and other arguments.

- direction
Character string, “out” bases the measure on outgoing ties,
“in” on incoming ties, and "all" on either/the sum of the two.
For two-mode networks, "all" uses as numerator the sum of differences
between the maximum centrality score for the mode
against all other centrality scores in the network,
whereas "in" uses as numerator the sum of differences
between the maximum centrality score for the mode
against only the centrality scores of the other nodes in that mode.

## Functions

`network_degree()`

: Calculate the degree centralization for a graph

`network_closeness()`

: Calculate the closeness centralization for a graph

`network_betweenness()`

: Calculate the betweenness centralization for a graph

`network_eigenvector()`

: Calculate the eigenvector centralization for a graph

## Examples

```
network_degree(ison_southern_women, direction = "in")
#> Mode 1 Mode 2
#> 0.231 0.466
network_closeness(ison_southern_women, direction = "in")
#> Mode 1 Mode 2
#> 0.214 0.528
network_betweenness(ison_southern_women, direction = "in")
#> Mode 1 Mode 2
#> 0.0668 0.1982
network_eigenvector(mpn_elite_mex)
#> [1] 0.63
network_eigenvector(ison_southern_women)
#> Mode 1 Mode 2
#> 0.0849 0.2630
```