Characterizing large online social networks (OSNs) through node querying is a challenging task. OSNs often impose severe constraints on the query rate, hence limiting the sample size to a small fraction of the total network. Various ad-hoc subgraph sampling methods have been proposed, but many of them give biased estimates and no theoretical basis on the accuracy. In this work, we focus on developing sampling methods for OSNs where querying a node also reveals partial structural information about its neighbors. Our methods are optimized for NoSQL graph databases (if the database can be accessed directly), or utilize Web API available on most major OSNs for graph sampling. We show that our sampling method has provable convergence guarantees on being an unbiased estimator, and it is more accurate than current state-of-the-art methods. We characterize metrics such as node label density estimation and edge label density estimation, two of the most fundamental network characteristics from which other network characteristics can be derived. We evaluate our methods on-the-fly over several live networks using their native APIs. Our simulation studies over a variety of offline datasets show that by including neighborhood information, our method drastically (4-fold) reduces the number of samples required to achieve the same estimation accuracy of state-of-the-art methods.
The Metropolis-Hasting RW (MHRW) @cite_20 modifies the RW procedure, aimed at sampling nodes with equal probability. However, in Ribeiro and Towsley @cite_27 we prove that MHRW degree distribution estimates perform poorly in comparison to RWs, more markedly for large degree nodes whose error grows proportionally to the degree value. Empirically, the accuracy of RW and MHRW has beeen compared in @cite_21 @cite_32 and, as predicted by our theoretical results, RW is consistently more accurate than MHRW.
@cite_27 @cite_21 @cite_32 @cite_20
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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. 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. short-lived or high degree peers due to the dynamics of peer participation or the heterogeneity of peer degrees, respectively. This paper presents Respondent-Driven Sampling (RDS) as a promising technique for sampling unstructured P2P overlays. This allows one to accurately estimate the distribution of a desired peer property without capturing the entire overlay structure. RDS is a variant of snowball sampling that has been proposed and used in the social sciences to characterize hidden population in a society [9], [13]. We apply the RDS technique to unstructured P2P network and evaluate its performance over a wide range of static and dynamic graphs as well as a widely deployed P2P system. Throughout our evaluation, we compare and contrast the performance of the RDS technique with another sampling technique, namely Metropolized Random Walk (MRW), that we developed in our earlier work [16]. Our main findings can be summarized as follows: First, RDS outperforms MRW across all scenarios. In particular, RDS exhibits a significantly better performance than MRW when the overlay structure exhibits a combination of highly skewed node degrees and highly skewed (local) clustering coefficients. Second, our simulation and empirical evaluations reveal that both the RDS and MRW techniques can accurately estimate key peer properties over dynamic unstructured overlays. Third, our empirical evaluations suggest that the efficiency of the two sampling techniques in practice is lower than in our simulations involving synthetic graphs. We attribute this to our inability to capture accurate reference snapshots. The rest of the paper is organized as follows: Section II presents an overview of both the RDS and MRW techniques, and sketches our evaluation methodology. We examine both techniques over variety of static and dynamic graphs in Section III and IV, respectively. Section V presents the empirical evaluation of the two sampling techniques over Gnutella network. 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.