  We consider the line graph of a simplicial complex. We prove that, as in the
case of line graphs of simple graphs, one can compute the second graded Betti
number of the facet ideal of a pure simplicial complex in terms of the
combinatorial structure of its line graph. We also give a characterization of
those graphs which are line graphs of some pure simplicial complex. In the end,
we consider pure simplicial complexes which are chordal and study their
relation to chordal line graphs.
