  We demonstrate that continuous time quantum walks on several types of
branching graphs, including graphs with loops, are identical to quantum walks
on simpler linear chain graphs. We also show graph types for which such
equivalence does not exist. Several instructive examples are discussed, and a
general approach to analyze more complex branching graphs is formulated. It is
further illustrated with a return quantum walk solution for a cube graph with
adjustable complex hopping amplitudes.
