`R/measure_centrality.R`

`degree_centrality.Rd`

These functions calculate common centrality measures for one- and two-mode networks.
All measures attempt to use as much information as they are offered,
including whether the networks are directed, weighted, or multimodal.
If this would produce unintended results,
first transform the salient properties using e.g. `to_undirected()`

functions.
All centrality and centralization measures return normalized measures by default,
including for two-mode networks.

```
node_degree(
.data,
normalized = TRUE,
alpha = 0,
direction = c("all", "out", "in")
)
node_outdegree(.data, normalized = TRUE, alpha = 0)
node_indegree(.data, normalized = TRUE, alpha = 0)
tie_degree(.data, normalized = TRUE)
network_degree(.data, normalized = TRUE, direction = c("all", "out", "in"))
network_outdegree(.data, normalized = TRUE)
network_indegree(.data, normalized = TRUE)
```

- .data
An object of a

`{manynet}`

-consistent class:matrix (adjacency or incidence) from

`{base}`

Redgelist, a data frame from

`{base}`

R or tibble from`{tibble}`

igraph, from the

`{igraph}`

packagenetwork, from the

`{network}`

packagetbl_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.

- alpha
Numeric scalar, the positive tuning parameter introduced in Opsahl et al (2010) for trading off between degree and strength centrality measures. By default,

`alpha = 0`

, which ignores tie weights and the measure is solely based upon degree (the number of ties).`alpha = 1`

ignores the number of ties and provides the sum of the tie weights as strength centrality. Values between 0 and 1 reflect different trade-offs in the relative contributions of degree and strength to the final outcome, with 0.5 as the middle ground. Values above 1 penalise for the number of ties. Of two nodes with the same sum of tie weights, the node with fewer ties will obtain the higher score. This argument is ignored except in the case of a weighted network.- 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.

A single centralization score if the object was one-mode, and two centralization scores if the object was two-mode.

Depending on how and what kind of an object is passed to the function,
the function will return a `tidygraph`

object where the nodes have been updated

`node_degree()`

: Calculates the degree centrality of nodes in an unweighted network, or weighted degree/strength of nodes in a weighted network.`node_outdegree()`

: Wraps node_degree(..., direction = "out")`node_indegree()`

: Wraps node_degree(..., direction = "in")`tie_degree()`

: Calculate the degree centrality of edges in a network`network_degree()`

: Calculate the degree centralization for a graph`network_outdegree()`

: Wraps network_degree(..., direction = "out")`network_indegree()`

: Wraps network_degree(..., direction = "out")

Faust, Katherine. 1997.
"Centrality in affiliation networks."
*Social Networks* 19(2): 157-191.
doi:10.1016/S0378-8733(96)00300-0
.

Borgatti, Stephen P., and Martin G. Everett. 1997.
"Network analysis of 2-mode data."
*Social Networks* 19(3): 243-270.
doi:10.1016/S0378-8733(96)00301-2
.

Borgatti, Stephen P., and Daniel S. Halgin. 2011.
"Analyzing affiliation networks."
In *The SAGE Handbook of Social Network Analysis*,
edited by John Scott and Peter J. Carrington, 417–33.
London, UK: Sage.
doi:10.4135/9781446294413.n28
.

Opsahl, Tore, Filip Agneessens, and John Skvoretz. 2010.
"Node centrality in weighted networks: Generalizing degree and shortest paths."
*Social Networks* 32, 245-251.
doi:10.1016/j.socnet.2010.03.006

`to_undirected()`

for removing edge directions
and `to_unweighted()`

for removing weights from a graph.

Other measures:
`between_centrality`

,
`close_centrality`

,
`closure`

,
`cohesion()`

,
`diffusion`

,
`eigenv_centrality`

,
`features`

,
`heterogeneity`

,
`hierarchy`

,
`holes`

Other centrality:
`between_centrality`

,
`close_centrality`

,
`eigenv_centrality`

```
node_degree(mpn_elite_mex)
#> Trevino Madero Carranza Aguilar Obregon Calles `Aleman Gonzalez` `Portes Gil`
#> 1 0.088 0.176 0.235 0.176 0.176 0.176 0.147 0.235
#> # ... with 27 more values from this nodeset unprinted. Use `print(..., n = Inf)` to print all values.
node_degree(ison_southern_women)
#> EVELYN LAURA THERESA BRENDA CHARLOTTE FRANCES ELEANOR PEARL RUTH VERNE MYRA
#> 1 0.571 0.5 0.571 0.5 0.286 0.286 0.286 0.214 0.286 0.286 0.286
#> # ... with 7 more values from this nodeset unprinted. Use `print(..., n = Inf)` to print all values.
#> E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 E11 E12 E13
#> 1 0.167 0.167 0.333 0.222 0.444 0.444 0.556 0.778 0.667 0.333 0.222 0.389 0.222
#> # ... with 1 more values from this nodeset unprinted. Use `print(..., n = Inf)` to print all values.
tie_degree(ison_adolescents)
#> `Betty-Sue` `Sue-Alice` `Alice-Jane` `Sue-Dale` `Alice-Dale` `Jane-Dale`
#> 1 0.333 0.667 0.444 0.556 0.556 0.333
#> # ... with 4 more values from this nodeset unprinted. Use `print(..., n = Inf)` to print all values.
network_degree(ison_southern_women, direction = "in")
#> Mode 1 Mode 2
#> 0.231 0.466
```