rel_is_reflexive {agop} R Documentation

## Reflexive Binary Relations

### Description

A binary relation R is reflexive, iff for all x we have xRx.

### Usage

```rel_is_reflexive(R)

rel_closure_reflexive(R)

rel_reduction_reflexive(R)
```

### Arguments

 `R` an object coercible to a 0-1 (logical) square matrix, representing a binary relation on a finite set.

### Details

`rel_is_reflexive` finds out if a given binary relation is reflexive. The function just checks whether all elements on the diagonal of `R` are non-zeros, i.e., it has O(n) time complexity, where n is the number of rows in `R`. Missing values on the diagonal may result in `NA`.

A reflexive closure of a binary relation R, determined by `rel_closure_reflexive`, is the minimal reflexive superset R' of R.

A reflexive reduction of a binary relation R, determined by `rel_reduction_reflexive`, is the minimal subset R' of R, such that the reflexive closures of R and R' are equal i.e., the largest irreflexive relation contained in R.

### Value

The `rel_closure_reflexive` and `rel_reduction_reflexive` functions return a logical square matrix. `dimnames` of `R` are preserved.

On the other hand, `rel_is_reflexive` returns a single logical value.

Other binary_relations: `check_comonotonicity`, `pord_nd`, `pord_spread`, `pord_weakdom`, `rel_graph`, `rel_is_antisymmetric`, `rel_is_asymmetric`, `rel_is_cyclic`, `rel_is_irreflexive`, `rel_is_symmetric`, `rel_is_total`, `rel_is_transitive`, `rel_reduction_hasse`