In order to efficiently study the characteristics of network domains and support development of network systems (e.g. algorithms, protocols that operate on networks), it is often necessary to sample a representative subgraph from a large complex network. Although recent subgraph sampling methods have been shown to work well, they focus on sampling from memory-resident graphs and assume that the sampling algorithm can access the entire graph in order to decide which nodes edges to select. Many large-scale network datasets, however, are too large and or dynamic to be processed using main memory (e.g., email, tweets, wall posts). In this work, we formulate the problem of sampling from large graph streams. We propose a streaming graph sampling algorithm that dynamically maintains a representative sample in a reservoir based setting. We evaluate the efficacy of our proposed methods empirically using several real-world data sets. Across all datasets, we found that our method produce samples that preserve better the original graph distributions.
Due to the popularity of online social networks such as Facebook and Twitter, there has been a lot of work @cite_34 @cite_2 @cite_25 @cite_19 @cite_33 @cite_36 studying the growth and evolution of these networks. While most of them have been on static graphs, recent works @cite_29 @cite_24 have started focusing on interactions in social networks. There is also work on decentralized search and crawling @cite_38 @cite_37 @cite_41 , however, in our work we focus on sampling from graphs that are naturally evolving as a stream of edges. In the literature, the most closely related efforts are that of Leskovec al in @cite_12 and Hubler al in @cite_21 . But, as we mentioned before, our work is different as we focus on the novel problem of sampling from graphs that are naturally evolving as a stream of edges (graph streams).
@cite_38 @cite_37 @cite_33 @cite_36 @cite_41 @cite_29 @cite_21 @cite_24 @cite_19 @cite_2 @cite_34 @cite_25 @cite_12
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Platforms such as Twitter have provided researchers with ample opportunities to analytically study social phenomena. There are however, significant computational challenges due to the enormous rate of production of new information: researchers are therefore, often forced to analyze a judiciously selected “sample” of the data. Like other social media phenomena, information diffusion is a social process–it is affected by user context, and topic, in addition to the graph topology. This paper studies the impact of different attribute and topology based sampling strategies on the discovery of an important social media phenomena–information diffusion. We examine several widely-adopted sampling methods that select nodes based on attribute (random, location, and activity) and topology (forest fire) as well as study the impact of attribute based seed selection on topology based sampling. Then we develop a series of metrics for evaluating the quality of the sample, based on user activity (e.g. volume, number of seeds), topological (e.g. reach, spread) and temporal characteristics (e.g. rate). We additionally correlate the diffusion volume metric with two external variables–search and news trends. Our experiments reveal that for small sample sizes (30 ), a sample that incorporates both topology and user context (e.g. location, activity) can improve on naive methods by a significant margin of 15-20 . Given multimillion-node graphs such as "who-follows-whom", "patent-cites-patent", "user-likes-page" and "actor director-makes-movie" networks, how can we find unexpected behaviors? When companies operate on the graphs with monetary incentives to sell Twitter "Followers" and Facebook page "Likes", the graphs show strange connectivity patterns. In this paper, we study a complete graph from a large Twitter-style social network, spanning up to 3.33 billion edges. We report strange deviations from typical patterns like smooth degree distributions. We find that such deviations are often due to "lockstep behavior" that large groups of followers connect to the same groups of followees. Our first contribution is that we study strange patterns on the adjacency matrix and in the spectral subspaces with respect to several flavors of lockstep. We discover that (a) the lockstep behaviors on the graph shape dense "block" in its adjacency matrix and creates "rays" in spectral subspaces, and (b) partially overlapping of the behaviors shape "staircase" in its adjacency matrix and creates "pearls" in spectral subspaces. The second contribution is that we provide a fast algorithm, using the discovery as a guide for practitioners, to detect users who offer the lockstep behaviors in undirected directed bipartite graphs. We carry out extensive experiments on both synthetic and real datasets, as well as public datasets from IMDb and US Patent. The results demonstrate the scalability and effectiveness of our proposed algorithm. By increasing the popularity of social networking websites like Facebook and Twitter, analysis of the structure of these networks receives significant attentions. The most important part of these analyses is towards detecting communities. The aforementioned structures are known with extremely high inter-connections versus few intra-connections in the graphs. In this paper, we have addressed the community detection problem by a novel framework based on Information Diffusion Model and Shapley Value Concept. Here, each node of the underlying graph is attributed to a rational agent trying to maximize its Shapley Value in the form of information it receives. Nash equilibrium of the game corresponds to the community structure of the graph. Compared with other methods, our approach demonstrates promising results on the well-known real world and synthetic graphs. The identification of popular and important topics discussed in social networks is crucial for a better understanding of societ al concerns. It is also useful for users to stay on top of trends without having to sift through vast amounts of shared information. Trend detection methods introduced so far have not used the network topology and has thus not been able to distinguish viral topics from topics that are diffused mostly through the news media. To address this gap, we propose two novel structural trend definitions we call coordinated and uncoordinated trends that use friendship information to identify topics that are discussed among clustered and distributed users respectively. Our analyses and experiments show that structural trends are significantly different from traditional trends and provide new insights into the way people share information online. We also propose a sampling technique for structural trend detection and prove that the solution yields in a gain in efficiency and is within an acceptable error bound. Experiments performed on a Twitter data set of 41.7 million nodes and 417 million posts show that even with a sampling rate of 0.005, the average precision is 0.93 for coordinated trends and 1 for uncoordinated trends.