  Many real-world networks are prohibitively large for data retrieval, storage
and analysis of all of its nodes and links. Understanding the structure and
dynamics of these networks entails creating a smaller representative sample of
the full graph while preserving its relevant topological properties. In this
report, we show that graph sampling algorithms currently proposed in the
literature are not able to preserve network properties even with sample sizes
containing as many as 20% of the nodes from the original graph. We present a
new sampling algorithm, called Tiny Sample Extractor, with a new goal of a
sample size smaller than 5% of the original graph while preserving two key
properties of a network, the degree distribution and its clustering
co-efficient. Our approach is based on a new empirical method of estimating
measurement biases in crawling algorithms and compensating for them
accordingly. We present a detailed comparison of best known graph sampling
algorithms, focusing in particular on how the properties of the sample
subgraphs converge to those of the original graph as they grow. These results
show that our sampling algorithm extracts a smaller subgraph than other
algorithms while also achieving a closer convergence to the degree
distribution, measured by the degree exponent, of the original graph. The
subgraph generated by the Tiny Sample Extractor, however, is not necessarily
representative of the full graph with regard to other properties such as
assortativity. This indicates that the problem of extracting a truly
representative small subgraph from a large graph remains unsolved.
