  We present the first combinatorial proof of the Graham-Pollak Formula for the
determinant of the distance matrix of a tree, via sign-reversing involutions
and the Lindstr\"om-Gessel-Viennot Lemma. Our approach provides a cohesive and
unified framework for the understanding of the existing generalizations and
$q$-analogues of the Graham-Pollak Formula, and facilitates the derivation of a
natural simultaneous generalizations for them.
