The difference between Directed edge and Edge

When used as nouns, directed edge means an edge of a directed graph, whereas edge means the boundary line of a surface.

Edge is also verb with the meaning: to move an object slowly and carefully in a particular direction.

check bellow for the other definitions of Directed edge and Edge

Edge as a noun:

The boundary line of a surface.
Edge as a noun (geometry):

A one-dimensional face of a polytope. In particular, the joining line between two vertices of a polygon; the place where two faces of a polyhedron meet.
Edge as a noun:

An advantage.

Examples:

"I have the edge on him."
Edge as a noun (also, _, figuratively):

The thin cutting side of the blade of an instrument, such as an ax, knife, sword, or scythe; that which cuts as an edge does, or wounds deeply, etc.
Edge as a noun:

A sharp terminating border; a margin; a brink; an extreme verge.

Examples:

"The cup is right on the edge of the table."

"He is standing on the edge of a precipice."
Edge as a noun:

Sharpness; readiness or fitness to cut; keenness; intenseness of desire.
Edge as a noun:

The border or part adjacent to the line of division; the beginning or early part (of a period of time)

Examples:

"in the edge of evening"
Edge as a noun (cricket):

A shot where the ball comes off the edge of the bat, often unintentionally.
Edge as a noun (graph theory):

A connected pair of vertices in a graph.
Edge as a noun:

In male masturbation, a level of sexual arousal that is maintained just short of reaching the point of inevitability, or climax; see also edging.

Edge as a verb (transitive):

To move an object slowly and carefully in a particular direction.

Examples:

"He edged the book across the table."
Edge as a verb (intransitive):

To move slowly and carefully in a particular direction.

Examples:

"He edged away from her."
Edge as a verb (usually in the form 'just edge'):

To win by a small margin.
Edge as a verb (cricket, transitive):

To hit the ball with an edge of the bat, causing a fine deflection.
Edge as a verb (transitive):

To trim the margin of a lawn where the grass meets the sidewalk, usually with an electric or gas-powered lawn edger.
Edge as a verb (transitive):

To furnish with an edge; to construct an edging.
Edge as a verb:

To furnish with an edge, as a tool or weapon; to sharpen.
Edge as a verb (figurative):

To make sharp or keen; to incite; to exasperate; to goad; to urge or egg on.
Edge as a verb (intransitive):

To delay one's orgasm so as to remain almost at the point of orgasm.