multiplex (version 1.5)

ltlw: First- and Last Letter Laws

Description

Find the First- and Last Letter Laws in the semigroup of relations.

Usage

ltlw(x)

Arguments

x

an object from the `Semigroup' class.

Value

• S
  the semigroup of relations.
• strings
  the strings of relations in the semigroup.
• First.Letter
  the First.Letters in rows and columns
• Last.Letter
  the Last.Letters in rows and columns

Details

The First- and Last Letter Laws of the semigroup of relations correspond to the right and left zero of the semigroup, and it has some consequences in the interpretation of the results of the relational structure of the network. This function depends on the semigroup of a (recommended) labeled set of relationships.

References

Lorrain, F. R�seaux sociaux et classifications sociales. Hermann, Paris. 1975.

See Also

semigroup, strings.

Examples

## Create the data: 3 binary relations among 3 elements
arr <- round( replace( array(runif(27), c(3,3,3)), array(runif(27),
       c(3,3,3))>.75, 1 ) )

## Put labels
dimnames(arr)[[3]] <- list("n","m","�")

## Construct the semigroup
S <- semigroup(arr, type="symbolic")

## Find the Letter Laws
ltlw(S)