all eigenvalues of the adjacency matrix formula_1 of a line graph are at least −2. the reason for this is that formula_1 can be written as formula_3, where formula_4 is the signless incidence matrix of the pre-line graph and formula_5 is the identity. in particular, formula_6 is the gramian matrix of a system of vectors: all graphs with this property have been called generalized line graphs.