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.
With global topology, @cite_12 discussed sampling techniques like random node, random edge, random subgraph in large graphs. @cite_22 introduced Albatross sampling which combines random jump and MHRW. @cite_26 also demonstrated true uniform sampling method among the users' id as ground-truth".
@cite_26 @cite_22 @cite_12
2137135938 2146008005
With more than 250 million active users, Facebook (FB) is currently one of the most important online social networks. Our goal in this paper is to obtain a representative (unbiased) sample of Facebook users by crawling its social graph. In this quest, we consider and implement several candidate techniques. Two approaches that are found to perform well are the Metropolis-Hasting random walk (MHRW) and a re-weighted random walk (RWRW). Both have pros and cons, which we demonstrate through a comparison to each other as well as to the "ground-truth" (UNI - obtained through true uniform sampling of FB userIDs). In contrast, the traditional Breadth-First-Search (BFS) and Random Walk (RW) perform quite poorly, producing substantially biased results. In addition to offline performance assessment, we introduce online formal convergence diagnostics to assess sample quality during the data collection process. We show how these can be used to effectively determine when a random walk sample is of adequate size and quality for subsequent use (i.e., when it is safe to cease sampling). Using these methods, we collect the first, to the best of our knowledge, unbiased sample of Facebook. Finally, we use one of our representative datasets, collected through MHRW, to characterize several key properties of Facebook. Given a huge real graph, how can we derive a representative sample? There are many known algorithms to compute interesting measures (shortest paths, centrality, betweenness, etc.), but several of them become impractical for large graphs. Thus graph sampling is essential.The natural questions to ask are (a) which sampling method to use, (b) how small can the sample size be, and (c) how to scale up the measurements of the sample (e.g., the diameter), to get estimates for the large graph. The deeper, underlying question is subtle: how do we measure success?.We answer the above questions, and test our answers by thorough experiments on several, diverse datasets, spanning thousands nodes and edges. We consider several sampling methods, propose novel methods to check the goodness of sampling, and develop a set of scaling laws that describe relations between the properties of the original and the sample.In addition to the theoretical contributions, the practical conclusions from our work are: Sampling strategies based on edge selection do not perform well; simple uniform random node selection performs surprisingly well. Overall, best performing methods are the ones based on random-walks and "forest fire"; they match very accurately both static as well as evolutionary graph patterns, with sample sizes down to about 15 of the original graph.