Definition of Arc in Graph Theory

 I have always used the term "arc" to refer to a line drawn between two nodes to represent a relationship between the nodes in a diagram.  I never meant it to be directional.  I apologize if people were confused.  In graph theory, an arc is defined as "an ordered pair."  That means it has direction -- the arc (A-B) is different from the arc (B-A), even if we do not include an arrowhead or some other notation.  How confusing!  There is some inconsistency in graph theory, since they use the term "directed" graph or digraph when the arcs all have a direction.  Then they always draw the arcs as an arrow... go figure.

I suppose I could be using "line" or "edge" which would be more correct in graph theory.

Well, I am not about to go back an revise everything I have written or in data model diagrams I have ever drawn!  So be advised.  When I say "arc" or draw one between two nodes, it never implies directionality. If direction is important I have always included some additional notation to indicate the direction, as for cardinality, a physical pointer, or a predicate reading.