  We introduce a new digraph width measure called directed branch-width. To do
this, we generalize a characterization of graph classes of bounded tree-width
in terms of their line graphs to digraphs. Although we prove that underlying
branch-width cannot be bounded in terms of our new measure, we show that
directed branch-width is a natural generalization of its undirected counterpart
and indeed the two invariants can be related via the operation of identifying
pairs of sources or pairs of sinks. Leveraging these operations and the
relationship to underlying tree-width allows us to extend a range of
algorithmic results from directed graphs with bounded underlying treewidth to
the larger class of digraphs having bounded directed branch-width.
