Counting the frequencies of 3-, 4-, and 5-node undirected motifs (also know as graphlets) is widely used for understanding complex networks such as social and biology networks. However, it is a great challenge to compute these metrics for a large graph due to the intensive computation. Despite recent efforts to count triangles (i.e., 3-node undirected motif counting), little attention has been given to developing scalable tools that can be used to characterize 4- and 5-node motifs. In this paper, we develop computational efficient methods to sample and count 4- and 5- node undirected motifs. Our methods provide unbiased estimators of motif frequencies, and we derive simple and exact formulas for the variances of the estimators. Moreover, our methods are designed to fit vertex centric programming models, so they can be easily applied to current graph computing systems such as Pregel and GraphLab. We conduct experiments on a variety of real-word datasets, and experimental results show that our methods are several orders of magnitude faster than the state-of-the-art methods under the same estimation errors.
In this paper, we study the problem of computing 4- and 5-node motifs' frequencies for , which is much different from the problem of computing the number of subgraph patterns appearing in studied in @cite_2 . Recently, a lot of efforts has been devoted to design sampling methods for computing a large graph's motif concentrations @cite_13 @cite_0 @cite_8 @cite_29 @cite_1 @cite_19 . However, these methods fail to compute motif frequencies, which is more fundamental than motif concentrations. @cite_22 propose the color-coding method to reduce the computational cost of counting subgraphs. Color coding reduces the computations by coloring nodes randomly and enumerating only colorful CISes (i.e., CISes that are consisted of nodes with distinct colors), but @cite_16 reaveals that the color-coding method is not scalable and is hindered by the sheer number of colorful CISes. @cite_28 @cite_5 @cite_21 @cite_3 develop sampling methods to estimate the number of triangles of static and dynamic graphs. @cite_26 develop sampling methods to estimate 4-node undirected motifs' frequencies. However their methods are edge centric methods, which cannot be easily applied to current vertex centric graph computing systems such as GraphLab @cite_10 and GraphChi @cite_4 . Moreover, their methods fail to sample and count 5-node motifs.
@cite_26 @cite_4 @cite_22 @cite_8 @cite_28 @cite_10 @cite_29 @cite_21 @cite_1 @cite_3 @cite_0 @cite_19 @cite_2 @cite_5 @cite_16 @cite_13
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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. 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 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. 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 ...