Alter composition

Number of alters of each node in each category, for categories that can overlap (Everett and Borgatti, 2026).

Usage

alter_composition(A, B, proportion = FALSE)

Arguments

A

A matrix of the ties of the nodes (rows) with their alters (columns)

B

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

proportion

Whether to divide each row by its sum, giving the proportion of the alters in each category

Value

This function returns a matrix of the nodes (rows) and the categories (columns).

Details

The memberships B are made row-stochastic, so that each row gives the proportion of a node that belongs to each category (for instance, the proportion of time spent on each project). The alter composition is the product \(AB\): for a partition, it counts the alters of each node in each category; with overlapping categories, it gives the extent to which the alters of each node belong to each category. The rows of \(AB\) add up to the degree of each node. A need not be square: its columns should be the rows of B, as in a matrix of respondents and the alters they named.

References

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

A <- matrix(c(
  0, 1, 1, 0,
  1, 0, 1, 1,
  1, 1, 0, 0,
  0, 1, 0, 0
), byrow = TRUE, ncol = 4)
rownames(A) <- colnames(A) <- c("a", "b", "c", "d")

# A partition
alter_composition(A, c("x", "x", "y", "y"))
#>   x y
#> a 1 1
#> b 1 2
#> c 2 0
#> d 1 0

# Overlapping categories: hours spent on two projects
B <- matrix(c(
  10, 0,
  5, 5,
  0, 8,
  2, 6
), byrow = TRUE, ncol = 2)
alter_composition(A, B)
#>     G1   G2
#> a 0.50 1.50
#> b 1.25 1.75
#> c 1.50 0.50
#> d 0.50 0.50