  Often, due to prohibitively large size or to limits to data collecting APIs,
it is not possible to work with a complete network dataset and sampling is
required. A type of sampling which is consistent with Twitter API restrictions
is uniform edge sampling. In this paper, we propose a methodology for the
recovery of two fundamental network properties from an edge-sampled network:
the degree distribution and the triangle count (we estimate the totals for the
network and the counts associated with each edge). We use a Bayesian approach
and show a range of methods for constructing a prior which does not require
assumptions about the original network. Our approach is tested on two synthetic
and three real datasets with diverse sizes, degree distributions, degree-degree
correlations and triangle count distributions.
