Let G be a geometric graph whose vertex set S is a set of n points in ℝ ^d . The stretch factor of two distinct points p and q in S is the ratio of their shortest-path distance in G and their Euclidean distance. We consider the problem of approximating the sum of all ((n) || 2)n \choose 2 stretch factors determined by all pairs of points in S. We show that for paths, cycles, and trees, this sum can be approximated, within a factor of 1 + ε, in O(n polylog(n)) time. For plane graphs, we present a (2 + ε)-approximation algorithm with running time O(n ^5/3 polylog(n)), and a (4 + ε)-approximation algorithm with running time O(n ^3/2 polylog(n)).