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.
Maiya and Berger-Wolf @cite_33 empirically investigates the performance of a number of subgraph sampling methods (e.g., breadth-first search, random walks, etc.) and their performance in respect to various topological properties (e.g., degree, clustering coefficient). Maiya and Berger-Wolf, however, does not use neighborhood information to improve the estimators or provide convergence guarantees. The literature also shows a variety of subgraph sampling works without convergence or accuracy guarantees @cite_28 @cite_3 , which have been empirically tested over a variety of networks. The above works @cite_33 @cite_28 @cite_3 also consider subgraph sampling techniques that can preserve other metrics, such as the eigenvalues of the original network @cite_28 , but without accuracy guarantees.
@cite_28 @cite_33 @cite_3
2146008005 2157747946
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. While data mining in chemoinformatics studied graph data with dozens of nodes, systems biology and the Internet are now generating graph data with thousands and millions of nodes. Hence data mining faces the algorithmic challenge of coping with this significant increase in graph size: Classic algorithms for data analysis are often too expensive and too slow on large graphs. While one strategy to overcome this problem is to design novel efficient algorithms, the other is to 'reduce' the size of the large graph by sampling. This is the scope of this paper: We will present novel Metropolis algorithms for sampling a 'representative' small subgraph from the original large graph, with 'representative' describing the requirement that the sample shall preserve crucial graph properties of the original graph. In our experiments, we improve over the pioneering work of Leskovec and Faloutsos (KDD 2006), by producing representative subgraph samples that are both smaller and of higher quality than those produced by other methods from the literature.