An edge automorphism \(\lambda\) of a nonempty graph G is called induced if there is a vertex automorphism \(\alpha\) of G such that \(\lambda (e)=\alpha (x)\alpha (y)\) for each edge \(e=xy\) of G. A nonempty graph G is line-symmetric if for all edges e and f of G there is some induced edge automorphism \(\lambda\) for which \(\lambda (e)=f.\) The authors investigate the structure of line-symmetric graphs.