In this paper, we address the problem of evaluating historical queries on graphs. To this end, we investigate the use of graph deltas, i.e., a log of time-annotated graph operations. Our storage model maintains the current graph snapshot and the delta. We reconstruct past snapshots by applying appropriate parts of the graph delta on the current snapshot. Query evaluation proceeds on the reconstructed snapshots but we also propose algorithms based mostly on deltas for efficiency. We introduce various techniques for improving performance, including materializing intermediate snapshots, partial reconstruction and indexing deltas.
There is also a large body of work that studies the evolution of real-world networks over time. In @cite_13 , it was shown that for a variety of real-world networks, graph density increases following a power-low and the graph diameter shrinks. Works on specific networks such as Flickr @cite_8 and Facebook @cite_9 also study network growth and their results can be exploited to enrich our model.
@cite_9 @cite_13 @cite_8
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Social networks are popular platforms for interaction, communication and collaboration between friends. Researchers have recently proposed an emerging class of applications that leverage relationships from social networks to improve security and performance in applications such as email, web browsing and overlay routing. While these applications often cite social network connectivity statistics to support their designs, researchers in psychology and sociology have repeatedly cast doubt on the practice of inferring meaningful relationships from social network connections alone. This leads to the question: Are social links valid indicators of real user interaction? If not, then how can we quantify these factors to form a more accurate model for evaluating socially-enhanced applications? In this paper, we address this question through a detailed study of user interactions in the Facebook social network. We propose the use of interaction graphs to impart meaning to online social links by quantifying user interactions. We analyze interaction graphs derived from Facebook user traces and show that they exhibit significantly lower levels of the "small-world" properties shown in their social graph counterparts. This means that these graphs have fewer "supernodes" with extremely high degree, and overall network diameter increases significantly as a result. To quantify the impact of our observations, we use both types of graphs to validate two well-known social-based applications (RE and SybilGuard). The results reveal new insights into both systems, and confirm our hypothesis that studies of social applications should use real indicators of user interactions in lieu of social graphs. How do real graphs evolve over time? What are "normal" growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large network, or in a very small number of snapshots; these include heavy tails for in- and out-degree distributions, communities, small-world phenomena, and others. However, given the lack of information about network evolution over long periods, it has been hard to convert these findings into statements about trends over time.Here we study a wide range of real graphs, and we observe some surprising phenomena. First, most of these graphs densify over time, with the number of edges growing super-linearly in the number of nodes. Second, the average distance between nodes often shrinks over time, in contrast to the conventional wisdom that such distance parameters should increase slowly as a function of the number of nodes (like O(log n) or O(log(log n)).Existing graph generation models do not exhibit these types of behavior, even at a qualitative level. We provide a new graph generator, based on a "forest fire" spreading process, that has a simple, intuitive justification, requires very few parameters (like the "flammability" of nodes), and produces graphs exhibiting the full range of properties observed both in prior work and in the present study. How do real graphs evolve over timeq What are normal growth patterns in social, technological, and information networksq Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large network or in a very small number of snapshots; these include heavy tails for in- and out-degree distributions, communities, small-world phenomena, and others. However, given the lack of information about network evolution over long periods, it has been hard to convert these findings into statements about trends over time. Here we study a wide range of real graphs, and we observe some surprising phenomena. First, most of these graphs densify over time with the number of edges growing superlinearly in the number of nodes. Second, the average distance between nodes often shrinks over time in contrast to the conventional wisdom that such distance parameters should increase slowly as a function of the number of nodes (like O(log n) or O(log(log n)). Existing graph generation models do not exhibit these types of behavior even at a qualitative level. We provide a new graph generator, based on a forest fire spreading process that has a simple, intuitive justification, requires very few parameters (like the flammability of nodes), and produces graphs exhibiting the full range of properties observed both in prior work and in the present study. We also notice that the forest fire model exhibits a sharp transition between sparse graphs and graphs that are densifying. Graphs with decreasing distance between the nodes are generated around this transition point. Last, we analyze the connection between the temporal evolution of the degree distribution and densification of a graph. We find that the two are fundamentally related. We also observe that real networks exhibit this type of relation between densification and the degree distribution. The rapid growth in the volume of many real-world graphs (e.g., social networks, web graphs, and spatial networks) has led to the development of various vertex-centric distributed graph computing systems in recent years. However, real-world graphs from different domains have very different characteristics, which often create bottlenecks in vertex-centric parallel graph computation. We identify three such important characteristics from a wide spectrum of real-world graphs, namely (1)skewed degree distribution, (2)large diameter, and (3)(relatively) high density. Among them, only (1) has been studied by existing systems, but many real-world power-law graphs also exhibit the characteristics of (2) and (3). In this paper, we propose a block-centric framework, called Blogel, which naturally handles all the three adverse graph characteristics. Blogel programmers may think like a block and develop efficient algorithms for various graph problems. We propose parallel algorithms to partition an arbitrary graph into blocks efficiently, and block-centric programs are then run over these blocks. Our experiments on large real-world graphs verified that Blogel is able to achieve orders of magnitude performance improvements over the state-of-the-art distributed graph computing systems. With the tremendous amount of research publications, recommending relevant papers to researchers to fulfill their information need becomes a significant problem. The major challenge to be tackled by our work is that given a target paper, how to effectively recommend a set of relevant papers from an existing citation network. In this paper, we propose a novel method to address the problem by incorporating various citation relations for a proper set of papers, which are more relevant but with a very limited size. The proposed method has two unique properties. Firstly, a metric called Local Relation Strength is defined to measure the dependency between cited and citing papers. Secondly, a model called Global Relation Strength is proposed to capture the relevance between two papers in the whole citation graph. We evaluate our proposed model on a real-world publication dataset and conduct an extensive comparison with the state-of-the-art baseline methods. The experimental results demonstrate that our method can have a promising improvement over the state-of-the-art techniques. In a document network such as a citation network of scientific documents, web-logs, etc., the content produced by authors exhibits their interest in certain topics. In addition some authors influence other authors' interests. In this work, we propose to model the influence of cited authors along with the interests of citing authors. Moreover, we hypothesize that apart from the citations present in documents, the context surrounding the citation mention provides extra topical information about the cited authors. However, associating terms in the context to the cited authors remains an open problem. We propose novel document generation schemes that incorporate the context while simultaneously modeling the interests of citing authors and influence of the cited authors. Our experiments show significant improvements over baseline models for various evaluation criteria such as link prediction between document and cited author, and quantitatively explaining unseen text. 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. Citation relationship between scientific publications has been successfully used for scholarly bibliometrics, information retrieval and data mining tasks, and citation-based recommendation algorithms are well documented. While previous studies investigated citation relations from various viewpoints, most of them share the same assumption that, if paper1 cites paper2 (or author1 cites author2), they are connected, regardless of citation importance, sentiment, reason, topic, or motivation. However, this assumption is oversimplified. In this study, we employ an innovative "context-rich heterogeneous network" approach, which paves a new way for citation recommendation task. In the network, we characterize 1) the importance of citation relationships between citing and cited papers, and 2) the topical citation motivation. Unlike earlier studies, the citation information, in this paper, is characterized by citation textual contexts extracted from the full-text citing paper. We also propose algorithm to cope with the situation when large portion of full-text missing information exists in the bibliographic repository. Evaluation results show that, context-rich heterogeneous network can significantly enhance the citation recommendation performance. This paper studies k-plexes, a well known pseudo-clique model for network communities. In a k-plex, each node can miss at most k-1 links. Our goal is to detect large communities in today's real-world graphs which can have hundreds of millions of edges. While many have tried, this task has been elusive so far due to its computationally challenging nature: k-plexes and other pseudo-cliques are harder to find and more numerous than cliques, a well known hard problem. We present D2K, which is the first algorithm able to find large k-plexes of very large graphs in just a few minutes. The good performance of our algorithm follows from a combination of graph-theoretical concepts, careful algorithm engineering and a high-performance implementation. In particular, we exploit the low degeneracy of real-world graphs, and the fact that large enough k-plexes have diameter 2. We validate a sequential and a parallel distributed implementation of D2K on real graphs with up to half a billion edges. Abstract Documents in computer-readable form can be used to provide information about other documents, i.e. those they cite. To do this efficiently requires procedures for computer recognition of citing statements. This is not easy, especially for multi-sentence citing statements. Computer recognition procedures have been developed which are accurate to the following extent: 73 of the words in statements selected by computer procedures as being citing statements are words which are correctly attributable to the corresponding documents. The retrieval effectiveness of computer-recognized citing statements was tested in the following way. First, for eight retrieval requests in inorganiic chemistry, average recall by search of Chemical Abstracts Service indexing and Chemical Abstracts abstract text words was found to be 50 . Words from citing statements referring to the papers to be retrieved were then added to the index terms and abstract words as additional access points, and searching was repeated. Average recall increased to 70 . Only words from citing statements published within a year of the cited papers were used. The retrieval effect of citing statement words alone (published within a year) without index or abstract terms was the following: average recall was 40 . When just the words of the titles of the cited papers were added to those citing statement words, average recall increased to 50 . A new form of document coupling called co-citation is defined as the frequency with which two documents are cited together. The co-citation frequency of two scientific papers can be determined by comparing lists of citing documents in the Science Citation Index and counting identical entries. Networks of co-cited papers can be generated for specific scientific specialties, and an example is drawn from the literature of particle physics. Co-citation patterns are found to differ significantly from bibliographic coupling patterns, but to agree generally with patterns of direct citation. Clusters of co-cited papers provide a new way to study the specialty structure of science. They may provide a new approach to indexing and to the creation of SDI profiles. A citing sentence is one that appears in a scientific article and cites previous work. Citing sentences have been studied and used in many applications. For example, they have been used in scientific paper summarization, automatic survey generation, paraphrase identification, and citation function classification. Citing sentences that cite multiple papers are common in scientific writing. This observation should be taken into consideration when using citing sentences in applications. For instance, when a citing sentence is used in a summary of a scientific paper, only the fragments of the sentence that are relevant to the summarized paper should be included in the summary. In this paper, we present and compare three different approaches for identifying the fragments of a citing sentence that are related to a given target reference. Our methods are: word classification, sequence labeling, and segment classification. Our experiments show that segment classification achieves the best results. Real world complex networks are scale free and possess meso-scale properties like core-periphery and community structure. We study evolution of the core over time in real world networks. This paper proposes evolving models for both unweighted and weighted scale free networks having local and global core-periphery as well as community structure. Network evolves using topological growth, self growth, and weight distribution function. To validate the correctness of proposed models, we use K-shell and S-shell decomposition methods. Simulation results show that the generated unweighted networks follow power law degree distribution with droop head and heavy tail. Similarly, generated weighted networks follow degree, strength, and edge-weight power law distributions. We further study other properties of complex networks, such as clustering coefficient, nearest neighbor degree, and strength degree correlation. We introduce and study the spectral evolution model, which characterizes the growth of large networks in terms of the eigenvalue decomposition of their adjacency matrices: In large networks, changes over time result in a change of a graph's spectrum, leaving the eigenvectors unchanged. We validate this hypothesis for several large social, collaboration, authorship, rating, citation, communication and tagging networks, covering unipartite, bipartite, signed and unsigned graphs. Following these observations, we introduce a link prediction algorithm based on the extrapolation of a network's spectral evolution. This new link prediction method generalizes several common graph kernels that can be expressed as spectral transformations. In contrast to these graph kernels, the spectral extrapolation algorithm does not make assumptions about specific growth patterns beyond the spectral evolution model. We thus show that it performs particularly well for networks with irregular, but spectral, growth patterns. Given large, multimillion-node graphs (e.g., Facebook, Web-crawls, etc.), how do they evolve over time? How are they connected? What are the central nodes and the outliers? In this article we define the Radius plot of a graph and show how it can answer these questions. However, computing the Radius plot is prohibitively expensive for graphs reaching the planetary scale. There are two major contributions in this article: (a) We propose HADI (HAdoop DIameter and radii estimator), a carefully designed and fine-tuned algorithm to compute the radii and the diameter of massive graphs, that runs on the top of the Hadoop MapReduce system, with excellent scale-up on the number of available machines (b) We run HADI on several real world datasets including YahooWeb (6B edges, 1 8 of a Terabyte), one of the largest public graphs ever analyzed. Thanks to HADI, we report fascinating patterns on large networks, like the surprisingly small effective diameter, the multimodal bimodal shape of the Radius plot, and its palindrome motion over time. Purpose – The purpose of this paper is to suggest an alternative to the widely used Times Cited criterion for analysing citation networks. The approach involves taking account of the natures of the papers that cite a given paper, so as to differentiate between papers that attract the same number of citations.Design methodology approach – ArticleRank is an algorithm that has been derived from Google's PageRank algorithm to measure the influence of journal articles. ArticleRank is applied to two datasets – a citation network based on an early paper on webometrics, and a self‐citation network based on the 19 most cited papers in the Journal of Documentation – using citation data taken from the Web of Knowledge database.Findings – ArticleRank values provide a different ranking of a set of papers from that provided by the corresponding Times Cited values, and overcomes the inability of the latter to differentiate between papers with the same numbers of citations. The difference in rankings between Times Cited ... Classical papers are of great help for beginners to get familiar with a new research area. However, digging them out is a difficult problem. This paper proposes Claper, a novel academic recommendation system based on two proven principles: the Principle of Download Persistence and the Principle of Citation Approaching (we prove them based on real-world datasets). The principle of download persistence indicates that classical papers have few decreasing download frequencies since they were published. The principle of citation approaching indicates that a paper which cites a classical paper is likely to cite citations of that classical paper. Our experimental results based on large-scale real-world datasets illustrate Claper can effectively recommend classical papers of high quality to beginners and thus help them enter their research areas. The old Asian legend about the blind men and the elephant comes to mind when looking at how different authors of scientific papers describe a piece of related prior work. It turns out that different citations to the same paper often focus on different aspects of that paper and that neither provides a full description of its full set of contributions. In this article, we will describe our investigation of this phenomenon. We studied citation summaries in the context of research papers in the biomedical domain. A citation summary is the set of citing sentences for a given article and can be used as a surrogate for the actual article in a variety of scenarios. It contains information that was deemed by peers to be important. Our study shows that citation summaries overlap to some extent with the abstracts of the papers and that they also differ from them in that they focus on different aspects of these papers than do the abstracts. In addition to this, co-cited articles (which are pairs of articles cited by another article) tend to be similar. We show results based on a lexical similarity metric called cohesion to justify our claims. © 2008 Wiley Periodicals, Inc. results on the spectra of adjacency matrices corresponding to models of real-world graphs. We find that when the number of links grows as the number of nodes, the spectral density of uncorrelated random matrices does not converge to the semicircle law. Furthermore, the spectra of real-world graphs have specific features, depending on the details of the corresponding models. In particular, scale-free graphs develop a trianglelike spectral density with a power-law tail, while small-world graphs have a complex spectral density consisting of several sharp peaks. These and further results indicate that the spectra of correlated graphs represent a practical tool for graph classification and can provide useful insight into the relevant structural properties of real networks. Extracting dense subgraphs from large graphs is a key primitive in a variety of graph mining applications, ranging from mining social networks and the Web graph to bioinformatics [41]. In this paper we focus on a family of poly-time solvable formulations, known as the k-clique densest subgraph problem (k-Clique-DSP) [57]. When k=2, the problem becomes the well-known densest subgraph problem (DSP) [22, 31, 33, 39]. Our main contribution is a sampling scheme that gives densest subgraph sparsifier, yielding a randomized algorithm that produces high-quality approximations while providing significant speedups and improved space complexity. We also extend this family of formulations to bipartite graphs by introducing the (p,q)-biclique densest subgraph problem ((p,q)-Biclique-DSP), and devise an exact algorithm that can treat both clique and biclique densities in a unified way. As an example of performance, our sparsifying algorithm extracts the 5-clique densest subgraph --which is a large-near clique on 62 vertices-- from a large collaboration network. Our algorithm achieves 100 accuracy over five runs, while achieving an average speedup factor of over 10,000. Specifically, we reduce the running time from ∼2 107 seconds to an average running time of 0.15 seconds. We also use our methods to study how the k-clique densest subgraphs change as a function of time in time-evolving networks for various small values of k. We observe significant deviations between the experimental findings on real-world networks and stochastic Kronecker graphs, a random graph model that mimics real-world networks in certain aspects. We believe that our work is a significant advance in routines with rigorous theoretical guarantees for scalable extraction of large near-cliques from networks.