We introduce a "derandomized" analogue of graph squaring. This
operation increases the connectivity of the graph (as measured by the
second eigenvalue) almost as well as squaring the graph does, yet only
increases the degree of the graph by a constant factor, instead of
squaring the degree.

One application of this product is an alternative proof of Reingold's
recent breakthrough result that S-T Connectivity in Undirected Graphs
can be solved in deterministic logspace.