  We consider estimating the edge-probability matrix of a network generated
from a graphon model when the full network is not observed---only some
overlapping subgraphs are. We extend the neighbourhood smoothing (NBS)
algorithm of Zhang et al. (2017) to this missing-data set-up and show
experimentally that, for a wide range of graphons, the extended NBS algorithm
achieves significantly smaller error rates than standard graphon estimation
algorithms such as vanilla neighbourhood smoothing (NBS), universal singular
value thresholding (USVT), blockmodel approximation, matrix completion, etc. We
also show that the extended NBS algorithm is much more robust to missing data.
