  Whitney's Theorem states that every graph, different from $K_3$ or $K_{1,3}$,
is uniquely determined by its line graph. A $1$-line graph of a multi-graph is
the graph with as vertices the edges of the multi-graph, and two edges adjacent
if and only if there is a unique vertex on both edges. The $\geq 1$-line graph
of a multi-graph is the graph on the edges of the multi-graph, where two edges
are adjacent if and only if there is at least one vertex on both edges. We
extend Whitney's theorem to such line graphs of multi-graphs, and show that
most multi-graphs are uniquely determined by their line graph. Moreover, we
present an algorithm to determine for a given graph $\Gamma$, if possible, a
multi-graph with $\Gamma$ as line graph.
