  Given a measurement graph $G= (V,E)$ and an unknown signal $r \in
\mathbb{R}^n$, we investigate algorithms for recovering $r$ from pairwise
measurements of the form $r_i - r_j$; $\{i,j\} \in E$. This problem arises in a
variety of applications, such as ranking teams in sports data and time
synchronization of distributed networks. Framed in the context of ranking, the
task is to recover the ranking of $n$ teams (induced by $r$) given a small
subset of noisy pairwise rank offsets. We propose a simple SVD-based
algorithmic pipeline for both the problem of time synchronization and ranking.
We provide a detailed theoretical analysis in terms of robustness against both
sampling sparsity and noise perturbations with outliers, using results from
matrix perturbation and random matrix theory. Our theoretical findings are
complemented by a detailed set of numerical experiments on both synthetic and
real data, showcasing the competitiveness of our proposed algorithms with other
state-of-the-art methods.
