ltlw: First- and Last Letter Laws

In mplex/multiplex: Algebraic Tools for the Analysis of Multiple Social Networks

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.

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.

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

Note

Since this function is based on the semigroup construction, see the Warning section and look at other details in the semigroup function section.

Author(s)

Antonio Rivero Ostoic

References

Lorrain, F. Réseaux 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","ñ")

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

## Find the Letter Laws
ltlw(S)

mplex/multiplex documentation built on April 9, 2024, 3:12 a.m.