  Statistical inference using pairwise comparison data is an effective approach
to analyzing large-scale sparse networks. In this paper, we propose a general
framework to model the mutual interactions in a network, which enjoys ample
flexibility in terms of model parametrization. Under this setup, we show that
the maximum likelihood estimator for the latent score vector of the subjects is
uniformly consistent under a near-minimal condition on network sparsity. This
condition is sharp in terms of the leading order asymptotics describing the
sparsity. Our analysis utilizes a novel chaining technique and illustrates an
important connection between graph topology and model consistency. Our results
guarantee that the maximum likelihood estimator is justified for estimation in
large-scale pairwise comparison networks where data are asymptotically
deficient. Simulation studies are provided in support of our theoretical
findings.
