Orders as Graphs
A
preorder
is a (reflexive,
connected
)
directed
graph
A
partial
order
is a (reflexive,
connected
)
directed
acyclic graph
A total
order
is a (reflexive,
connected
)
linear
directed
graph
An
equivalence relation
is a (reflexive) graph wherein all
components
are
connected
(These definitions are not checked)