strings {multiplex}

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, equat = FALSE, k = 2, smpl, valued)

Arguments

x

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

equat

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

k

length of the strings in the equations

smpl

(optional and logical) whether to simplify or not the string relations

valued

(logical) whether the strings are with a valued format

Details

The strings are the unique relations, which constitute 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.

Value

An object of 'Strings' class.

wt

the generators and compound relations

ord

the order of the structure

st

the labels of the unique relations

equat

the equations among strings of relations

Note

The maximum length of the strings in the equations is currently 4.

Author(s)

Antonio Rivero Ostoic

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.

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)