This paper introduces a novel algorithm for cardinality, i.e., the number of nodes, estimation in large scale anonymous graphs using statistical inference methods. Applications of this work include estimating the number of sensor devices, online social users, active protein cells, etc. In anonymous graphs, each node possesses little or non-existing information on the network topology. In particular, this paper assumes that each node only knows its unique identifier. The aim is to estimate the cardinality of the graph and the neighbours of each node by querying a small portion of them. While the former allows the design of more efficient coding schemes for the network, the second provides a reliable way for routing packets. As a reference for comparison, this work considers the Best Linear Unbiased Estimators (BLUE). For dense graphs and specific running times, the proposed algorithm produces a cardinality estimate proportional to the BLUE. Furthermore, for an arbitrary number of iterations, the estimate converges to the BLUE as the number of queried nodes tends to the total number of nodes in the network. Simulation results confirm the theoretical results by revealing that, for a moderate running time, asking a small group of nodes is sufficient to perform an estimation of 95 of the whole network.
@cite_16 @cite_20 propose a scheme for estimating the network parameters in directed graphs using random walks. Their algorithm precisely predicts the out-degree distributions of a variety of real-world graphs. Similarly, @cite_0 study the problem in a context of robust visual object recognition. The authors in @cite_2 present two algorithms for estimating the total number of online users in social networks by using sampling from graphs assumed to have a stationary distribution.
@cite_0 @cite_16 @cite_20 @cite_2
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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. Despite recent efforts to characterize complex networks such as citation graphs or online social networks (OSNs), little attention has been given to developing tools that can be used to characterize directed graphs in the wild, where no pre-processed data is available. The presence of hidden incoming edges but observable outgoing edges poses a challenge to characterize large directed graphs through crawling, as existing sampling methods cannot cope with hidden incoming links. The driving principle behind our random walk (RW) sampling method is to construct, in real-time, an undirected graph from the directed graph such that the random walk on the directed graph is consistent with one on the undirected graph. We then use the RW on the undirected graph to estimate the outdegree distribution. Our algorithm accurately estimates outdegree distributions of a variety of real world graphs. We also study the hardness of indegree distribution estimation when indegrees are latent (i.e., incoming links are only observed as outgoing edges). We observe that, in the same scenarios, indegree distribution estimates are highly innacurate unless the directed graph is highly symmetrical. Sampling from large graphs is an area of great interest, especially since the emergence of huge structures such as Online Social Networks (OSNs) and the World Wide Web (WWW). These networks, when viewed as graphs, often contain hundreds of millions of vertices and billions of edges. The large scale properties of a network can be summarized in terms of parameters of the underlying graph, such as the total number of vertices, edges and triangles. The large size of these networks makes it computationally expensive to obtain such structural properties of the underlying graph by exhaustive search. If we can estimate these properties by taking small but representative samples from the network, then size is no longer such a problem. In this paper we present a general framework to estimate network properties using random walks. These methods work under the assumption we are able to obtain local characteristics of a vertex during each step of the random walk, for example the number and labels of the neighboring vertices of a specific vertex These assumptions are relatively reasonable in practice, but may add some additional query cost to each step of the random walk. We also present some practical methods to estimate the total number of edges links m, number of vertices nodes n and number of connected triads of vertices (triangles) t in graphs with degree distributions which follow a power-law and higher number of triangles higher than expected in random graphs. We use these graphs since they tend to better correspond to the structure of large online networks, and in fact some of the data used are taken from such a network. Additionally we present experimental estimates for n, m, t we obtained using our methods on real or manufactured networks. In order to make the methods practical, the total number of steps made by the walk was limited to at most the size n of the network. In fact the results appear to converge for a lower number of steps, indicating that our proposed methods are feasible in practice. The popular h-index used to measure scientific output can be described in terms of a pool of evaluated objects (the papers), a quality function on the evaluated objects (the number of citations received by each paper) and a sentencing line crossing the origin, whose intersection with the graph of the quality function yields the index value (in the h-index this is a line with slope 1). Based on this abstraction, we present a new index, the c-index, in which the evaluated objects are the citations received by an author, a group of authors, a journal, etc., the quality function of a citation is the collaboration distance between the authors of the cited and the citing papers, and the sentencing line can take slopes between 0 and ∞. As a result, the new index counts only those citations which are significant enough, where significance is proportional to collaboration distance. Several advantages of the new c-index with respect to previous proposals are discussed. 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. 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. Patent prior art search is a type of search in the patent domain where documents are searched for that describe the work previously carried out related to a patent application. The goal of this search is to check whether the idea in the patent application is novel. Vocabulary mismatch is one of the main problems of patent retrieval which results in low retrievability of similar documents for a given patent application. In this paper we show how the term distribution of the cited documents in an initially retrieved ranked list can be used to address the vocabulary mismatch. We propose a method for query modeling estimation which utilizes the citation links in a pseudo relevance feedback set. We first build a topic dependent citation graph, starting from the initially retrieved set of feedback documents and utilizing citation links of feedback documents to expand the set. We identify the important documents in the topic dependent citation graph using a citation analysis measure. We then use the term distribution of the documents in the citation graph to estimate a query model by identifying the distinguishing terms and their respective weights. We then use these terms to expand our original query. We use CLEF-IP 2011 collection to evaluate the effectiveness of our query modeling approach for prior art search. We also study the influence of different parameters on the performance of the proposed method. The experimental results demonstrate that the proposed approach significantly improves the recall over a state-of-the-art baseline which uses the link-based structure of the citation graph but not the term distribution of the cited documents. An overwhelming number of news articles are available every day via the internet. Unfortunately, it is impossible for us to peruse more than a handful; furthermore it is difficult to ascertain an article’s social context, i.e., is it popular, what sorts of people are reading it, etc. In this paper, we develop a system to address this problem in the restricted domain of political news by harnessing implicit and explicit contextual information from the blogosphere. Specifically, we track thousands of blogs and the news articles they cite, collapsing news articles that have highly overlapping content. We then tag each article with the number of blogs citing it, the political orientation of those blogs, and the level of emotional charge expressed in the blog posts that link to the news article. We summarize and present the results to the user via a novel visualization which displays this contextual information; the user can then find the most popular articles, the articles most cited by liberals, the articles most emotionally discussed in the political blogosphere, etc. Scholars are increasingly citing electronic “web references” which are not preserved in libraries or full text archives. WebCite is a new standard for citing web references. To “webcite” a document involves archiving the cited Web page through www.webcitation.org and citing the WebCite permalink instead of (or in addition to) the unstable live Web page. This journal has amended its “instructions for authors” accordingly, asking authors to archive cited Web pages before submitting a manuscript. Almost 200 other journals are already using the system. We discuss the rationale for WebCite, its technology, and how scholars, editors, and publishers can benefit from the service. Citing scholars initiate an archiving process of all cited Web references, ideally before they submit a manuscript. Authors of online documents and websites which are expected to be cited by others can ensure that their work is permanently available by creating an archived copy using WebCite and providing the citation information including the WebCite link on their Web document(s). Editors should ask their authors to cache all cited Web addresses (Uniform Resource Locators, or URLs) “prospectively” before submitting their manuscripts to their journal. Editors and publishers should also instruct their copyeditors to cache cited Web material if the author has not done so already. Finally, WebCite can process publisher submitted “citing articles” (submitted for example as eXtensible Markup Language [XML] documents) to automatically archive all cited Web pages shortly before or on publication. Finally, WebCite can act as a focussed crawler, caching retrospectively references of already published articles. Copyright issues are addressed by honouring respective Internet standards (robot exclusion files, no-cache and no-archive tags). Long-term preservation is ensured by agreements with libraries and digital preservation organizations. The resulting WebCite Index may also have applications for research assessment exercises, being able to measure the impact of Web services and published Web documents through access and Web citation metrics. @PARASPLIT [J Med Internet Res 2005;7(5):e60] Random walk is an important tool in many graph mining applications including estimating graph parameters, sampling portions of the graph, and extracting dense communities. In this paper we consider the problem of sampling nodes from a large graph according to a prescribed distribution by using random walk as the basic primitive. Our goal is to obtain algorithms that make a small number of queries to the graph but output a node that is sampled according to the prescribed distribution. Focusing on the uniform distribution case, we study the query complexity of three algorithms and show a near-tight bound expressed in terms of the parameters of the graph such as average degree and the mixing time. Both theoretically and empirically, we show that some algorithms are preferable in practice than the others. We also extend our study to the problem of sampling nodes according to some polynomial function of their degrees; this has implications for designing efficient algorithms for applications such as triangle counting. 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. 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 ... Social networks provide interesting algorithmic properties that can be used to bootstrap the security of distributed systems. For example, it is widely believed that social networks are fast mixing, and many recently proposed designs of such systems make crucial use of this property. However, whether real-world social networks are really fast mixing is not verified before, and this could potentially affect the performance of such systems based on the fast mixing property. To address this problem, we measure the mixing time of several social graphs, the time that it takes a random walk on the graph to approach the stationary distribution of that graph, using two techniques. First, we use the second largest eigenvalue modulus which bounds the mixing time. Second, we sample initial distributions and compute the random walk length required to achieve probability distributions close to the stationary distribution. Our findings show that the mixing time of social graphs is much larger than anticipated, and being used in literature, and this implies that either the current security systems based on fast mixing have weaker utility guarantees or have to be less efficient, with less security guarantees, in order to compensate for the slower mixing. Networks are characterized by nodes and edges. While there has been a spate of recent work on estimating the number of nodes in a network, the edge-estimation question appears to be largely unaddressed. In this work we consider the problem of estimating the average degree of a large network using efficient random sampling, where the number of nodes is not known to the algorithm. We propose a new estimator for this problem that relies on access to node samples under a prescribed distribution. Next, we show how to efficiently realize this ideal estimator in a random walk setting. Our estimator has a natural and simple implementation using random walks; we bound its performance in terms of the mixing time of the underlying graph. We then show that our estimators are both provably and practically better than many natural estimators for the problem. Our work contrasts with existing theoretical work on estimating average degree, which assume that a uniform random sample of nodes is available and the number of nodes is known. Estimating characteristics of large graphs via sampling is a vital part of the study of complex networks. Current sampling methods such as (independent) random vertex and random walks are useful but have drawbacks. Random vertex sampling may require too many resources (time, bandwidth, or money). Random walks, which normally require fewer resources per sample, can suffer from large estimation errors in the presence of disconnected or loosely connected graphs. In this work we propose a new m-dimensional random walk that uses m dependent random walkers. We show that the proposed sampling method, which we call Frontier sampling, exhibits all of the nice sampling properties of a regular random walk. At the same time, our simulations over large real world graphs show that, in the presence of disconnected or loosely connected components, Frontier sampling exhibits lower estimation errors than regular random walks. We also show that Frontier sampling is more suitable than random vertex sampling to sample the tail of the degree distribution of the graph. 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. AbstractThis article presents algorithms for estimating the number of users in online social networks. Although such networks sometimes publish such statistics, there are good reasons to validate their reports. The proposed schemes can also estimate the cardinality of network subpopulations. Because this information is seldom voluntarily divulged, such algorithms must operate only by interacting with the social networks’ public Applications Programming Interfaces (APIs). No other external information can be assumed. Due to obvious traffic and privacy concerns, the number of such interactions is severely limited. We therefore focus on minimizing the number of API interactions needed for producing good-sized estimates.We adopt the standard abstraction of social networks as undirected graphs and perform random walk-based node sampling. By counting the number of collisions or nonunique nodes in the sample, we produce a size estimate. Then we show analytically that the estimate error vanishes with high probabi... 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 . 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. 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.