  Recovering global rankings from pairwise comparisons has wide applications
from time synchronization to sports team ranking. Pairwise comparisons
corresponding to matches in a competition can be construed as edges in a
directed graph (digraph), whose nodes represent e.g. competitors with an
unknown rank. In this paper, we introduce neural networks into the ranking
recovery problem by proposing the so-called GNNRank, a trainable GNN-based
framework with digraph embedding. Moreover, new objectives are devised to
encode ranking upsets/violations. The framework involves a ranking score
estimation approach, and adds an inductive bias by unfolding the Fiedler vector
computation of the graph constructed from a learnable similarity matrix.
Experimental results on extensive data sets show that our methods attain
competitive and often superior performance against baselines, as well as
showing promising transfer ability. Codes and preprocessed data are at:
\url{https://github.com/SherylHYX/GNNRank}.
