atomic reification as a (named) edge

In a recent meeting, someone (Adrian?) wanted us to write a short description  expressing the proposed rdf:reifies based reification in terms of other commonly understood concepts. Here is a description that uses the concept of "edge":

The proposed (new-style, well-formed) atomic reification can be thought of as an edge, directed from subject (of the triple-term) to the object (of the triple-term), labeled with the predicate (of the triple-term), and having a name.

Example:
The atomic reification :e rdf:reifies <<( :s :p :o )>>
can be thought of as:
a named, directed, labeled edge: connecting :s to :o, labeled with :p, and having the name :e.

For comparison, one could think of an RDF triple :s :p :o as:
an unnamed , directed, labeled edge: connecting :s to :o, labeled with :p.

Thanks,
Souri.