Line pseudodigraphs
Robert L. Hemminger, Joseph B. Klerlein · Journal of Graph Theory · 1977
Abstract A new definition of the line digraph is given that reflects all types of arc adjacencies in the original digraph. The definition also allows for loops and multiple arcs, hence it is called the line pseudodigraph. A Whitney type theorem is then given; that is, the relationship between pseudodigraphs having the same line pseudodigraph is determined.