  A projective rectangle is like a projective plane that may have different
lengths in two directions. We develop properties of the graph of lines, in
which adjacency means having a common point, especially its strong regularity
and clique structure. The main construction of projective rectangles, stated in
a previous paper, gives rectangles whose graph of lines is a known strongly
regular bilinear forms graph. That fact leads to a proof that the main
construction does produce projective rectangles, and also gives a new
representation of bilinear forms graphs. We conclude by mentioning a few simple
graph properties, such as the chromatic number, which is not known, and a
partial geometry obtained from the graph.
