# partial.order: The Partial Order of String relations or of Galois... In multiplex: Algebraic Tools for the Analysis of Multiple Social Networks

## Description

Construct the partial order table of unique relations of the semigroup, or else of the concepts produced by Galois derivations.

## Usage

 `1` ```partial.order(x, type = c("strings", "galois", "pi.rels"), lbs, sel, po.incl) ```

## Arguments

 `x` an object of a '`Strings`' or a '`Galois`' class `type` whether the object corresponds to string relations, Galois derivations, or π-relations `lbs` (optional) the labels of the unique relations `sel` (optional) selected elements in ‘x’ for the partial order `po.incl` (optional, works only with type `"pi.rels"`) should the partial order in the π-relations be included

## Details

To get the partial order of an entire semigroup, both generators and compound relations must be considered. This information and the labels of the unique relations are given by the `strings` function. cf. `semigroup` to see how the `x` should be specified properly.

Galois derivations are now possible to be partially ordered as well, and this option is based on the output given by the `galois` function.

## Value

An object of '`Partial.Order`' class with the partial order table in a matrix form.

## Author(s)

Antonio Rivero Ostoic

## References

Pattison, P.E. Algebraic Models for Social Networks. Cambridge University Press. 1993.

Ganter, B. and R. Wille Formal Concept Analysis - Mathematical Foundations. Springer. 1996.

`as.strings`, `strings`, `galois`, `perm`, `diagram`, `fltr`.
 ```1 2 3 4 5 6 7 8``` ```## Load the data, and obtain the partial order data("incubA") ## the strings in the structure st <- strings(incubA\$IM) ## Get the partial order partial.order(st) ```