  We develop a new sampling method to estimate eigenvector centrality on
incomplete networks. Our goal is to estimate this global centrality measure
having at disposal a limited amount of data. This is the case in many
real-world scenarios where data collection is expensive, the network is too big
for data storage capacity or only partial information is available. The
sampling algorithm is theoretically grounded by results derived from spectral
approximation theory. We studied the problem on both synthetic and real data
and tested the performance comparing with traditional methods, such as random
walk and uniform sampling. We show that approximations obtained from such
methods are not always reliable and that our algorithm, while preserving
computational scalability, improves performance under different error measures.
