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Partition of centrality by category

Source: R/categories.R
partition_centrality.Rd

Contribution of the nodes of each category to the centrality of every node (Everett and Borgatti, 2012, 2026).

Usage

partition_centrality(
  A,
  B,
  measure = c("betweenness", "degree"),
  digraph = TRUE,
  type = c("out", "in"),
  weighted = FALSE,
  alpha = 1
)

Arguments

A

A square matrix

B

A matrix of the membership of the nodes (rows) in the categories (columns), or a vector with the category of each node

measure

The centrality: betweenness (default) or degree

digraph

Whether the matrix is directed or undirected

type

For the degree of a directed network, out (default) or in

weighted

Whether the betweenness uses the values of the ties, as in betweenness_centrality()

alpha

The alpha parameter of Opsahl et al. (2010) for the weighted betweenness

Value

This function returns a matrix with the part of the centrality of each node (rows) contributed by each category (columns).

Details

The betweenness of a node \(v\) adds up the dependency of every source \(s\) on \(v\), \(\delta_s(v)\), the extent to which \(s\) needs \(v\) to reach the other nodes through shortest paths (Brandes, 2001). Grouping the sources by their category, \(D^T B\), splits the betweenness of each node into the parts contributed by each category, and with overlapping categories each source contributes in proportion to its memberships. The rows add up to the betweenness of betweenness_centrality().

The degree is split with the alter composition, \(AB\) for the out-degree and \(A^T B\) for the in-degree.

References

Brandes, U. (2001). A faster algorithm for betweenness centrality. Journal of Mathematical Sociology, 25(2), 163–177. doi:10.1080/0022250X.2001.9990249

Everett, M. G. and Borgatti, S. P. (2012). Categorical attribute based centrality: E–I and G–F centrality. Social Networks, 34(4), 562–569. doi:10.1016/j.socnet.2012.06.002

Everett, M. G. and Borgatti, S. P. (2026). Alter composition with overlapping group memberships. Social Networks, 85, 80–88. doi:10.1016/j.socnet.2025.12.001

Author

Alejandro Espinosa-Rada

Examples

data(campnet)
# Betweenness of the Camp 92 network split by the gender of the sources
partition_centrality(campnet$network, campnet$attributes$gender)
#>                 1         2
#> HOLLY   24.333333 54.000000
#> BRAZEY   0.000000  0.000000
#> CAROL    1.333333  0.000000
#> PAM      8.500000 24.000000
#> PAT     25.000000 14.500000
#> JENNIE   6.333333  0.000000
#> PAULINE  7.000000  5.500000
#> ANN      0.500000  0.000000
#> MICHAEL  9.000000 49.833333
#> BILL     0.000000  0.000000
#> LEE      0.000000  5.000000
#> DON     14.000000  2.333333
#> JOHN     0.000000  0.000000
#> HARRY    0.000000  2.333333
#> GERY    10.000000 44.666667
#> STEVE    6.000000 10.833333
#> BERT     6.000000  7.666667
#> RUSS    11.000000 36.333333