Alter heterogeneity

Blau's heterogeneity of the alters of each node, for categories that can overlap (Everett and Borgatti, 2026).

Usage

alter_heterogeneity(A, B, normalized = 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

normalized

Whether to return the IQV

Value

This function returns a vector with the heterogeneity of the alters of each node.

Details

The heterogeneity of a node is \(1 - \sum_k p_k^2\), where \(p_k\) is the proportion of its alters in category \(k\), taken from the rows of alter_composition() (Blau, 1977). A node with a single alter has some heterogeneity when that alter belongs to several categories. The IQV divides the index by its maximum, \(1 - 1/K\), where \(K\) is the number of categories. The nodes without alters are NA.

References

Blau, P. M. (1977). Inequality and heterogeneity: A primitive theory of social structure. Free Press.

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")
B <- matrix(c(
  10, 0,
  5, 5,
  0, 8,
  2, 6
), byrow = TRUE, ncol = 2)

alter_heterogeneity(A, B)
#>         a         b         c         d 
#> 0.3750000 0.4861111 0.3750000 0.5000000