multiplex (version 2.5)

strings: Strings of Relations

Description

Function to get the labels of the unique relations of the semigroup; that is the generators and compound relations that are the elements of the complete semigroup.

Usage

strings(x, smpl = FALSE, equat = FALSE, k = 2)

Arguments

x

an array; usually with three dimensions of stacked matrices where the multiple relations are placed.

smpl

(logical) whether to simplify or not the strings of relations

equat

(logical) should the equations be included in the output?

k

length of the strings

Value

An object of `Strings' class.

Details

The strings are the unique relations which constitutes the elements of the complete semigroup. These are both the generators and the compound relations after applying the Axiom of Quality, which means that even some generators can be disregarded.

This function is especially useful to construct the partial order of relations, and to establish the set of equations in the relational structure.

References

Boorman, S.A. and H.C. White, `Social Structure from Multiple Networks. II. Role Structures.' American Journal of Sociology, 81 (6), 1384-1446. 1976.

See Also

partial.order, semigroup, ltlw.

Examples

## Create the data: 2 binary relations among 3 elements
arr <- round( replace( array(runif(18), c(3,3,2)), array(runif(18),
       c(3,3,2))>.5, 1 ) )

## get the strings
strings(arr)