  In this paper, we propose new nonparametric approach to network inference
that may be viewed as a fusion of block sampling procedures for temporally and
spatially dependent processes with the classical network methodology. We
develop estimation and uncertainty quantification procedures for network mean
degree using a "patchwork" sample and nonparametric bootstrap, under the
assumption of unknown degree distribution. We investigate asymptotic properties
of the proposed patchwork bootstrap procedure and present cross-validation
methodology for selecting an optimal patch size. We validate the new patchwork
bootstrap on simulated networks with short and long tailed mean degree
distributions, and revisit the Erdos collaboration data to illustrate the
proposed methodology.
