  Ranking nodes based on their centrality stands a fundamental, yet,
challenging problem in large-scale networks. Approximate methods can quickly
estimate nodes' centrality and identify the most central nodes, but the ranking
for the majority of remaining nodes may be meaningless. For example, ranking
for less-known websites in search queries is known to be noisy and unstable. To
this end, we investigate a new node ranking problem with two important
distinctions: a) ranking quality, rather than the centrality estimation
quality, as the primary objective; and b) ranking only nodes of interest, e.g.,
websites that matched search criteria. We propose Sample space Partitioning
Hypothesis Ranking, or SaPHyRa, that transforms node ranking into a hypothesis
ranking in machine learning. This transformation maps nodes' centrality to the
expected risks of hypotheses, opening doors for theoretical machine learning
(ML) tools. The key of SaPHyRa is to partition the sample space into exact and
approximate subspaces. The exact subspace contains samples related to the nodes
of interest, increasing both estimation and ranking qualities. The approximate
space can be efficiently sampled with ML-based techniques to provide
theoretical guarantees on the estimation error. Lastly, we present SaPHyRa_bc,
an illustration of SaPHyRa on ranking nodes' betweenness centrality (BC). By
combining a novel bi-component sampling, a 2-hop sample partitioning, and
improved bounds on the Vapnik-Chervonenkis dimension, SaPHyRa_bc can
effectively rank any node subset in BC. Its performance is up to 200x faster
than state-of-the-art methods in approximating BC, while its rank correlation
to the ground truth is improved by multifold.
