Many online social networks feature restrictive web interfaces which only allow the query of a user's local neighborhood through the interface. To enable analytics over such an online social network through its restrictive web interface, many recent efforts reuse the existing Markov Chain Monte Carlo methods such as random walks to sample the social network and support analytics based on the samples. The problem with such an approach, however, is the large amount of queries often required (i.e., a long "mixing time") for a random walk to reach a desired (stationary) sampling distribution. In this paper, we consider a novel problem of enabling a faster random walk over online social networks by "rewiring" the social network on-the-fly. Specifically, we develop Modified TOpology (MTO)-Sampler which, by using only information exposed by the restrictive web interface, constructs a "virtual" overlay topology of the social network while performing a random walk, and ensures that the random walk follows the modified overlay topology rather than the original one. We show that MTO-Sampler not only provably enhances the efficiency of sampling, but also achieves significant savings on query cost over real-world online social networks such as Google Plus, Epinion etc.
The small world phenomenon, that consistently occurs in numerous exist- ing networks, refers to two similar but different properties — small average distance and the clustering effect. We consider a hybrid graph model that incorporates both properties by combining a global graph and a local graph. The global graph is modeled by a random graph with a power law degree distribution, while the local graph has specified local connectivity. We will prove that the hybrid graph has average distance and diameter close to that of random graphs with the same degree distribution (under certain mild conditions). We also give a simple decomposition algorithm which, for any given (real) graph, identifies the global edges and extracts the local graph (which is uniquely determined depending only on the local connectivity). We can then apply our theoretical results for analyzing real graphs, provided the parameters of the hybrid model can be appropriately chosen. Access to realistic, complex graph datasets is critical to research on social networking systems and applications. Simulations on graph data provide critical evaluation of new systems and applications ranging from community detection to spam filtering and social web search. Due to the high time and resource costs of gathering real graph datasets through direct measurements, researchers are anonymizing and sharing a small number of valuable datasets with the community. However, performing experiments using shared real datasets faces three key disadvantages: concerns that graphs can be de-anonymized to reveal private information, increasing costs of distributing large datasets, and that a small number of available social graphs limits the statistical confidence in the results. The use of measurement-calibrated graph models is an attractive alternative to sharing datasets. Researchers can "fit" a graph model to a real social graph, extract a set of model parameters, and use them to generate multiple synthetic graphs statistically similar to the original graph. While numerous graph models have been proposed, it is unclear if they can produce synthetic graphs that accurately match the properties of the original graphs. In this paper, we explore the feasibility of measurement-calibrated synthetic graphs using six popular graph models and a variety of real social graphs gathered from the Facebook social network ranging from 30,000 to 3 million edges. We find that two models consistently produce synthetic graphs with common graph metric values similar to those of the original graphs. However, only one produces high fidelity results in our application-level benchmarks. While this shows that graph models can produce realistic synthetic graphs, it also highlights the fact that current graph metrics remain incomplete, and some applications expose graph properties that do not map to existing metrics. 