  The statistical modeling of random networks has been widely used to uncover
interaction mechanisms in complex systems and to predict unobserved links in
real-world networks. In many applications, network connections are collected
via egocentric sampling: a subset of nodes is sampled first, after which all
links involving this subset are recorded; all other information is missing.
Compared with the assumption of ``uniformly missing at random", egocentrically
sampled partial networks require specially designed modeling strategies.
Current statistical methods are either computationally infeasible or based on
intuitive designs without theoretical justification. Here, we propose an
approach to fit general low-rank models for egocentrically sampled networks,
which include several popular network models. This method is based on graph
spectral properties and is computationally efficient for large-scale networks.
It results in consistent recovery of missing subnetworks due to egocentric
sampling for sparse networks. To our knowledge, this method offers the first
theoretical guarantee for egocentric partial network estimation in the scope of
low-rank models. We evaluate the technique on several synthetic and real-world
networks and show that it delivers competitive performance in link prediction
tasks.
