Most sampling techniques for online social networks (OSNs) are based on a particular sampling method on a single graph, which is referred to as a statistics. However, various realizing methods on different graphs could possibly be used in the same OSN, and they may lead to different sampling efficiencies, i.e., asymptotic variances. To utilize multiple statistics for accurate measurements, we formulate a mixture sampling problem, through which we construct a mixture unbiased estimator which minimizes asymptotic variance. Given fixed sampling budgets for different statistics, we derive the optimal weights to combine the individual estimators; given fixed total budget, we show that a greedy allocation towards the most efficient statistics is optimal. In practice, the sampling efficiencies of statistics can be quite different for various targets and are unknown before sampling. To solve this problem, we design a two-stage framework which adaptively spends a partial budget to test different statistics and allocates the remaining budget to the inferred best statistics. We show that our two-stage framework is a generalization of 1) randomly choosing a statistics and 2) evenly allocating the total budget among all available statistics, and our adaptive algorithm achieves higher efficiency than these benchmark strategies in theory and experiment.
Recently the most popular graph crawling is random walk-based sampling, including simple random walk with re-weighting (RWRW) @cite_18 @cite_15 and Metropolis-Hastings random walk (MHRW) @cite_0 . RWRW is considered as a special case of Respondent-Driven Sampling (RDS) @cite_18 if only one neighbor is chosen in each iteration and revisiting nodes is allowed. It is also biased to sample high degree nodes, but the bias can be corrected by the Hansen-Hurwitz estimator shown in @cite_7 @cite_16 . RWRW was not only used to sample OSNs @cite_17 @cite_8 , but also P2P networks and Web @cite_6 @cite_13 . MHRW is based on the Metropolis-Hastings (MH) algorithm and provides unbiased samples directly @cite_0 @cite_15 . Some studies @cite_18 @cite_15 have shown that RWRW estimates are more accurate than MHRW estimates.
@cite_18 @cite_7 @cite_8 @cite_6 @cite_0 @cite_15 @cite_16 @cite_13 @cite_17
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Graph sampling via crawling has been actively considered as a generic and important tool for collecting uniform node samples so as to consistently estimate and uncover various characteristics of complex networks. The so-called simple random walk with re-weighting (SRW-rw) and Metropolis-Hastings (MH) algorithm have been popular in the literature for such unbiased graph sampling. However, an unavoidable downside of their core random walks -- slow diffusion over the space, can cause poor estimation accuracy. In this paper, we propose non-backtracking random walk with re-weighting (NBRW-rw) and MH algorithm with delayed acceptance (MHDA) which are theoretically guaranteed to achieve, at almost no additional cost, not only unbiased graph sampling but also higher efficiency (smaller asymptotic variance of the resulting unbiased estimators) than the SRW-rw and the MH algorithm, respectively. In particular, a remarkable feature of the MHDA is its applicability for any non-uniform node sampling like the MH algorithm, but ensuring better sampling efficiency than the MH algorithm. We also provide simulation results to confirm our theoretical findings. Our goal in this paper is to develop a practical framework for obtaining a uniform sample of users in an online social network (OSN) by crawling its social graph. Such a sample allows to estimate any user property and some topological properties as well. To this end, first, we consider and compare several candidate crawling techniques. Two approaches that can produce approximately uniform samples 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." In contrast, using Breadth-First-Search (BFS) or an unadjusted Random Walk (RW) leads to substantially biased results. Second, and 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 diagnostics can be used to effectively determine when a random walk sample is of adequate size and quality. Third, as a case study, we apply the above methods to Facebook and we collect the first, to the best of our knowledge, representative sample of Facebook users. We make it publicly available and employ it to characterize several key properties of Facebook. Estimating characteristics of large graphs via sampling is vital in the study of complex networks. In this work, we study the Mean Squared Error (MSE) associated with different sampling methods for the degree distribution. These sampling methods include independent random vertex (RV) and random edge (RE) sampling, and crawling methods such as random walks (RWs) and the widely used Metropolis-Hastings algorithm for uniformly sampling vertices (MHRWu). We see that the RW MSE is upper bounded by a quantity that is proportional to the RE MSE and inversely proportional to the spectral gap of the RW transition probability matrix. We also determine conditions under which RW is preferable to RV. Finally, we present an approximation of the MHRWu MSE. We evaluate the accuracy of our approximations and bounds through simulations on large real world graphs. Twitter as one of the most important microblogging online social networks has attracted more than 200 million users in recent years. Although there have been several attempts on characterizing the Twitter by using incomplete sampled data, they have not been very successful to estimate the characteristics of the whole network. In this paper, we characterize Twitter by sampling from its social graph and user behaviors through a random walk based sampling technique called Respondent-Driven Sampling (RDS). To the best of our knowledge, for the first time RDS method and its estimator are used in order to obtain uniform unbiased estimation of several key structural and behavioral properties of Twitter. We compared the performance of the proposed method with other sampling methods such as Metropolis-Hasting Random Walk (MHRW) and sampling from active users (Timeline) against the uniform sampling (UNI). In order to gather the required data, we have implemented four independent crawlers. Our experimental results indicate that the RDS method exhibits lower estimation errors to the sample in- and out-degree distribution compared to MHRW and Timeline. We also show that RDS is more suitable to sample the followers vs. followings ratio, and the correlation between followers followings vs. tweets.