Sampling Online Social Networks via Heterogeneous Statistics

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

Towards Unbiased BFS Sampling

Breadth First Search (BFS) is a widely used approach for sampling large unknown Internet topologies. Its main advantage over random walks and other exploration techniques is that a BFS sample is a plausible graph on its own, and therefore we can study its topological characteristics. However, it has been empirically observed that incomplete BFS is biased toward high-degree nodes, which may strongly affect the measurements. In this paper, we first analytically quantify the degree bias of BFS sampling. In particular, we calculate the node degree distribution expected to be observed by BFS as a function of the fraction f of covered nodes, in a random graph RG(pk) with an arbitrary degree distribution pk. We also show that, for RG(pk), all commonly used graph traversal techniques (BFS, DFS, Forest Fire, Snowball Sampling, RDS) suffer from exactly the same bias. Next, based on our theoretical analysis, we propose a practical BFS-bias correction procedure. It takes as input a collected BFS sample together with its fraction f. Even though RG(pk) does not capture many graph properties common in real-life graphs (such as assortativity), our RG(pk)-based correction technique performs well on a broad range of Internet topologies and on two large BFS samples of Facebook and Orkut networks. Finally, we consider and evaluate a family of alternative correction procedures, and demonstrate that, although they are unbiased for an arbitrary topology, their large variance makes them far less effective than the RG(pk)-based technique.Comment: BFS, RDS, graph traversal, sampling bias correctio

On sampling social networking services

This article aims at summarizing the existing methods for sampling social networking services and proposing a faster confidence interval for related sampling methods. It also includes comparisons of common network sampling techniques

Bayesian Inference of Online Social Network Statistics via Lightweight Random Walk Crawls

Online social networks (OSN) contain extensive amount of information about the underlying society that is yet to be explored. One of the most feasible technique to fetch information from OSN, crawling through Application Programming Interface (API) requests, poses serious concerns over the the guarantees of the estimates. In this work, we focus on making reliable statistical inference with limited API crawls. Based on regenerative properties of the random walks, we propose an unbiased estimator for the aggregated sum of functions over edges and proved the connection between variance of the estimator and spectral gap. In order to facilitate Bayesian inference on the true value of the estimator, we derive the approximate posterior distribution of the estimate. Later the proposed ideas are validated with numerical experiments on inference problems in real-world networks