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Vog: Summarizing and understanding large graphs
, 2014
"... How can we succinctly describe a millionnode graph with a few simple sentences? How can we measure the ‘importance’ of a set of discovered subgraphs in a large graph? These are exactly the problems we focus on. Our main ideas are to construct a ‘vocabulary ’ of subgraphtypes that often occur in re ..."
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How can we succinctly describe a millionnode graph with a few simple sentences? How can we measure the ‘importance’ of a set of discovered subgraphs in a large graph? These are exactly the problems we focus on. Our main ideas are to construct a ‘vocabulary ’ of subgraphtypes that often occur in real graphs (e.g., stars, cliques, chains), and from a set of subgraphs, find the most succinct description of a graph in terms of this vocabulary. We measure success in a wellfounded way by means of the Minimum Description Length (MDL) principle: a subgraph is included in the summary if it decreases the total description length of the graph. Our contributions are threefold: (a) formulation: we provide a principled encoding scheme to choose vocabulary subgraphs; (b) algorithm: we develop VOG, an efficient method to minimize the description cost, and (c) applicability: we report experimental results on multimillionedge real graphs, including Flickr and the Notre Dame web graph. 1
Fast Robustness Estimation in Large Social Graphs: Communities and Anomaly Detection
"... Given a large social graph, like a scientific collaboration network, what can we say about its robustness? Can we estimate a robustness index for a graph quickly? If the graph evolves over time, how these properties change? In this work, we are trying to answer the above questions studying the expan ..."
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Given a large social graph, like a scientific collaboration network, what can we say about its robustness? Can we estimate a robustness index for a graph quickly? If the graph evolves over time, how these properties change? In this work, we are trying to answer the above questions studying the expansion properties of large social graphs. First, we present a measure which characterizes the robustness properties of a graph, and serves as global measure of the community structure (or lack thereof). We study how these properties change over time and we show how to spot outliers and anomalies over time. We apply our method on several diverse real networks with millions of nodes. We also show how to compute our measure efficiently by exploiting the special spectral properties of realworld networks.
Graphq: Graph query processing with abstraction refinement
 In USENIX ATC
, 2015
"... Abstract This paper introduces GraphQ, a scalable querying framework for very large graphs. GraphQ is built on a key insight that many interesting graph propertiessuch as finding cliques of a certain size, or finding vertices with a certain page rank can be effectively computed by exploring only a ..."
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Abstract This paper introduces GraphQ, a scalable querying framework for very large graphs. GraphQ is built on a key insight that many interesting graph propertiessuch as finding cliques of a certain size, or finding vertices with a certain page rank can be effectively computed by exploring only a small fraction of the graph, and traversing the complete graph is an overkill. The centerpiece of our framework is the novel idea of abstraction refinement, where the very large graph is represented as multiple levels of abstractions, and a query is processed through iterative refinement across graph abstraction levels. As a result, GraphQ enjoys several distinctive traits unseen in existing graph processing systems: query processing is naturally budgetaware, friendly for outofcore processing when "Big Graphs" cannot entirely fit into memory, and endowed with strong correctness properties on query answers. With GraphQ, a wide range of complex analytical queries over very large graphs can be answered with resources affordable to a single PC, which complies with the recent trend advocating singlemachinebased Big Data processing. Experiments show GraphQ can answer queries in graphs 46 times bigger than the memory capacity, only in several seconds to minutes. In contrast, GraphChi, a stateoftheart graph processing system, takes hours to days to compute a wholegraph solution. An additional comparison with a modified version of GraphChi that terminates immediately when a query is answered shows that GraphQ is on average 1.613.4× faster due to its ability to process partial graphs.
On Compressing Weighted Timeevolving Graphs
"... Existinggraphcompressiontechniquesmostlyfocusonstatic graphs. However for many practical graphs such as social networks the edge weights frequentlychange over time. This phenomenonraises thequestionof howtocompress dynamic graphs while maintaining most of their intrinsic structural patterns at each ..."
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Existinggraphcompressiontechniquesmostlyfocusonstatic graphs. However for many practical graphs such as social networks the edge weights frequentlychange over time. This phenomenonraises thequestionof howtocompress dynamic graphs while maintaining most of their intrinsic structural patterns at each time snapshot. In this paper we show that the encoding cost of a dynamic graph is proportional to the heterogeneity of a three dimensional tensor that represents the dynamic graph. We propose an effective algorithm that compresses a dynamic graph by reducing the heterogeneity of its tensor representation, and at the same time also maintains a maximum lossy compression error at any time stamp of the dynamic graph. The bounded compression error benefits compressed graphs in that they retain good approximationsoftheoriginal edgeweights, andhencepropertiesofthe original graph (such as shortest paths) are well preserved. To the best of our knowledge, this is the first work that compresses weighted dynamic graphs with bounded lossy compression error at any time snapshot of the graph.
Privacy Preservation by kAnonymization of Weighted Social Networks
"... Abstract—Privacy preserving analysis of a social network aims at a better understanding of the network and its behavior, while at the same time protecting the privacy of its individuals. We propose an anonymization method for weighted graphs, i.e., for social networks where the strengths of links ar ..."
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Abstract—Privacy preserving analysis of a social network aims at a better understanding of the network and its behavior, while at the same time protecting the privacy of its individuals. We propose an anonymization method for weighted graphs, i.e., for social networks where the strengths of links are important. This is in contrast with many previous studies which only consider unweighted graphs. Weights can be essential for social network analysis, but they pose new challenges to privacy preserving network analysis. In this paper, we mainly consider prevention of identity disclosure, but we also touch on edge and edge weight disclosure in weighted graphs. We propose a method that provides kanonymity of nodes against attacks where the adversary has information about the structure of the network, including its edge weights. The method is efficient, and it has been evaluated in terms of privacy and utility on real word datasets. I.
Lossy Compression of Dynamic, Weighted Graphs
"... Abstract—A graph is used to represent data in which the relationships between the objects in the data are at least as important as the objects themselves. Large graph datasets are becoming more common as networks such as the Internet grow, and our ability to measure these graphs improves. This neces ..."
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Abstract—A graph is used to represent data in which the relationships between the objects in the data are at least as important as the objects themselves. Large graph datasets are becoming more common as networks such as the Internet grow, and our ability to measure these graphs improves. This necessitates methods to compress these datasets. In this paper we present a method aimed at lossy compression of large, dynamic, weighted graphs. Keywordsgraph compression; dynamic, weighted graphs; shrinkage; I.
EgoNetCloud: Eventbased Egocentric Dynamic Network Visualization
"... Eventbased egocentric dynamic networks are an important class of networks widely seen in many domains. In this paper, we present a visual analytics approach for these networks by combining datadriven network simplifications with a novel visualization designEgoNetCloud. In particular, an integrate ..."
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Eventbased egocentric dynamic networks are an important class of networks widely seen in many domains. In this paper, we present a visual analytics approach for these networks by combining datadriven network simplifications with a novel visualization designEgoNetCloud. In particular, an integrated data processing pipeline is proposed to prune, compress and filter the networks into smaller but salient abstractions. To accommodate the simplified network into the visual design, we introduce a constrained graph layout algorithm on the dynamic network. Through a reallife case study as well as conversations with the domain expert, we demonstrate the effectiveness of the EgoNetCloud design and system in completing analysis tasks on eventbased dynamic networks. The user study comparing EgoNetCloud with a working system on academic search confirms the effectiveness and convenience of our visual analytics based approach. 1
On Compressing Weighted Timeevolving Graphs
"... Existing graph compression techniques mostly focus on static graphs. However for many practical graphs such as social networks the edge weights frequently change over time. This phenomenon raises the question of how to compress dynamic graphs while maintaining most of their intrinsic structural patt ..."
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Existing graph compression techniques mostly focus on static graphs. However for many practical graphs such as social networks the edge weights frequently change over time. This phenomenon raises the question of how to compress dynamic graphs while maintaining most of their intrinsic structural patterns at each time snapshot. In this paper we show that the encoding cost of a dynamic graph is proportional to the heterogeneity of a three dimensional tensor that represents the dynamic graph. We propose an effective algorithm that compresses a dynamic graph by reducing the heterogeneity of its tensor representation, and at the same time also maintains a maximum lossy compression error at any time stamp of the dynamic graph. The bounded compression error benefits compressed graphs in that they retain good approximations of the original edge weights, and hence properties of the original graph (such as shortest paths) are well preserved. To the best of our knowledge, this is the first work that compresses weighted dynamic graphs with bounded lossy compression error at any time snapshot of the graph.
TimeCrunch: Interpretable Dynamic Graph Summarization
"... How can we describe a large, dynamic graph over time? Is it random? If not, what are the most apparent deviations from randomness – a dense block of actors that persists over time, or perhaps a star with many satellite nodes that appears with some fixed periodicity? In practice, these deviations ..."
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How can we describe a large, dynamic graph over time? Is it random? If not, what are the most apparent deviations from randomness – a dense block of actors that persists over time, or perhaps a star with many satellite nodes that appears with some fixed periodicity? In practice, these deviations indicate patterns – for example, botnet attackers forming a bipartite core with their victims over the duration of an attack, family members bonding in a cliquelike fashion over a difficult period of time, or research collaborations forming and fading away over the years. Which patterns exist in realworld dynamic graphs, and how can we find and rank them in terms of importance? These are exactly the problems we focus on in this work. Our main contributions are (a) formulation: we show how to formalize this problem as minimizing the encoding cost in a data compression paradigm, (b) algorithm: we propose TIMECRUNCH, an effective, scalable and parameterfree method for finding coherent, temporal patterns in dynamic graphs and (c) practicality: we apply our method to several large, diverse realworld datasets with up to 36 million edges and 6.3 million nodes. We show that TIMECRUNCH is able to compress these graphs by summarizing important temporal structures and finds patterns that agree with intuition.