  The edge-bandwidth of a graph is the minimum, over all labelings of the edges
with distinct integers, of the maximum difference between labels of two
incident edges. We prove that edge-bandwidth is at least as large as bandwidth
for every graph, with equality for certain caterpillars. We obtain sharp or
nearly-sharp bounds on the change in edge-bandwidth under addition,
subdivision, or contraction of edges. We compute edge-bandwidth for cliques,
bicliques, caterpillars, and some theta graphs.
