A citation is a reference to a published or unpublished source. More a citation is an abbreviated alphanumeric expression embedded in the body of an intellectual work that denotes an entry in the bibliographic references section of the work for the purpose of acknowledging the relevance of the works of others to the topic of discussion at the spot where the citation appears; the combination of both the in-body citation and the bibliographic entry constitutes what is thought of as a citation. References to single, machine-readable assertions in electronic scientific articles are known as nanopublications, a form of microattribution. Citations have several important purposes: to uphold intellectual honesty, to attribute prior or unoriginal work and ideas to the correct sources, to allow the reader to determine independently whether the referenced material supports the author's argument in the claimed way, to help the reader gauge the strength and validity of the material the author has used.
As Roark and Emerson have argued, citations relate to the way authors perceive the substance of their work, their position in the academic system, the moral equivalency of their place and words. Despite these attributes, many drawbacks and shortcoming of citation practices have been reported, including for example honorary citations, circumstantial citations, discriminatory citations and arbitrary citations; the forms of citations subscribe to one of the accepted citations systems, such as the Oxford, Harvard, MLA, American Sociological Association, American Psychological Association, other citations systems, because their syntactic conventions are known and interpreted by readers. Each of these citation systems has its disadvantages. Editors specify the citation system to use. Bibliographies, other list-like compilations of references, are not considered citations because they do not fulfill the true spirit of the term: deliberate acknowledgement by other authors of the priority of one's ideas.
A bibliographic citation is a reference to a book, web page, or other published item. Citations should supply detail to identify the item uniquely. Different citation systems and styles are used in scientific citation, legal citation, prior art, the arts, the humanities. Citation content can vary depending on the type of source and may include: Book: author, book title, place of publication, date of publication, page number if appropriate. Journal: author, article title, journal title, date of publication, page number. Newspaper: author, article title, name of newspaper, section title and page number if desired, date of publication. Web site: author and publication title where appropriate, as well as a URL, a date when the site was accessed. Play: inline citations offer part and line numbers, the latter separated by periods: 4.452 refers to scene 4, line 452. For example, "In Eugene Onegin, Onegin rejects Tanya when she is free to be his, only decides he wants her when she is married". Poem: spaced slashes are used to indicate separate lines of a poem, parenthetical citations include the line number.
For example: "For I must love because I live / And life in me is what you give.". Interview: name of interviewer, interview descriptor and date of interview. Along with information such as author, date of publication and page numbers, citations may include unique identifiers depending on the type of work being referred to. Citations of books may include an International Standard Book Number. Specific volumes, articles or other identifiable parts of a periodical, may have an associated Serial Item and Contribution Identifier or an International Standard Serial Number. Electronic documents may have a digital object identifier. Biomedical research articles may have a PubMed Identifier. Broadly speaking, there are two types of citation systems, the Vancouver system and parenthetical referencing. However, the Council of Science Editors adds the citation-name system; the Vancouver system uses sequential numbers in either bracketed or superscript or both. The numbers refer to either endnotes that provide source detail.
The notes system may or may not require a full bibliography, depending on whether the writer has used a full-note form or a shortened-note form. For example, an excerpt from the text of a paper using a notes system without a full bibliography could look like: "The five stages of grief are denial, bargaining and acceptance."1The note, located either at the foot of the page or at the end of the paper would look like this: 1. Elisabeth Kübler-Ross, On Death and Dying 45–60. In a paper with a full bibliography, the shortened note might look like: 1. Kübler-Ross, On Death and Dying 45–60; the bibliography entry, required with a shortened note, would look like this: Kübler-Ross, Elisabeth. On Death and Dying. New York: Macmillan, 1969. In the humanities, many authors use footnotes or endnotes to supply anecdotal information. In this way, what looks like a citation is supplementary material, or suggestions for further reading. Parenthetical referencing known as Harvard referencing, has full or partial, in-text, citations enclosed in circular brackets and embedded in the paragraph.
An example of a parenthetical reference: "The five stages of grief are denial, bargai
PageRank is an algorithm used by Google Search to rank web pages in their search engine results. PageRank was named after one of the founders of Google. PageRank is a way of measuring the importance of website pages. According to Google: PageRank works by counting the number and quality of links to a page to determine a rough estimate of how important the website is; the underlying assumption is that more important websites are to receive more links from other websites. PageRank is not the only algorithm used by Google to order search results, but it is the first algorithm, used by the company, it is the best known. PageRank is a link analysis algorithm and it assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set; the algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is referred to as the PageRank of E and denoted by P R.
A PageRank results from a mathematical algorithm based on the webgraph, created by all World Wide Web pages as nodes and hyperlinks as edges, taking into consideration authority hubs such as cnn.com or usa.gov. The rank value indicates an importance of a particular page. A hyperlink to a page counts as a vote of support; the PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it. A page, linked to by many pages with high PageRank receives a high rank itself. Numerous academic papers concerning PageRank have been published since Page and Brin's original paper. In practice, the PageRank concept may be vulnerable to manipulation. Research has been conducted into identifying falsely influenced PageRank rankings; the goal is to find an effective means of ignoring links from documents with falsely influenced PageRank. Other link-based ranking algorithms for Web pages include the HITS algorithm invented by Jon Kleinberg,the IBM CLEVER project, the TrustRank algorithm and the Hummingbird algorithm.
The eigenvalue problem was suggested in 1976 by Gabriel Pinski and Francis Narin, who worked on scientometrics ranking scientific journals, in 1977 by Thomas Saaty in his concept of Analytic Hierarchy Process which weighted alternative choices, in 1995 by Bradley Love and Steven Sloman as a cognitive model for concepts, the centrality algorithm. Larry Page and Sergey Brin developed PageRank at Stanford University in 1996 as part of a research project about a new kind of search engine. Sergey Brin had the idea that information on the web could be ordered in a hierarchy by "link popularity": a page ranks higher as there are more links to it. Rajeev Motwani and Terry Winograd co-authored with Page and Brin the first paper about the project, describing PageRank and the initial prototype of the Google search engine, published in 1998: shortly after and Brin founded Google Inc. the company behind the Google search engine. While just one of many factors that determine the ranking of Google search results, PageRank continues to provide the basis for all of Google's web-search tools.
The name "PageRank" plays off of the name of developer Larry Page, as well as of the concept of a web page. The word is a trademark of Google, the PageRank process has been patented. However, the patent is assigned to Stanford University and not to Google. Google has exclusive license rights on the patent from Stanford University; the university received 1.8 million shares of Google in exchange for use of the patent. PageRank was influenced by citation analysis, early developed by Eugene Garfield in the 1950s at the University of Pennsylvania, by Hyper Search, developed by Massimo Marchiori at the University of Padua. In the same year PageRank was introduced, Jon Kleinberg published his work on HITS. Google's founders cite Garfield and Kleinberg in their original papers. A small search-engine called "RankDex" from IDD Information Services, designed by Robin Li, from 1996 exploring a similar strategy for site-scoring and page-ranking. Li patented the technology in RankDex in 1999 and used it when he founded Baidu in China in 2000.
Larry Page referenced Li's work in some of his U. S. patents for PageRank. The PageRank algorithm outputs a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. PageRank can be calculated for collections of documents of any size, it is assumed in several research papers that the distribution is evenly divided among all documents in the collection at the beginning of the computational process. The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more reflect the theoretical true value. A probability is expressed as a numeric value between 0 and 1. A 0.5 probability is expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank. Assume a small universe of four web pages: A, B, C and D. Links from a page to itself are ignored.
Multiple outbound links from one page to another page are treated as a single link. PageRank is initialized to the same value for all pages. In the original form of PageRank, the sum of PageRank over all pages was the total number of pages on the web at that time, so each page in this example would have an initial value of 1; however versions of PageRan
Web of Science
Web of Science is an online subscription-based scientific citation indexing service produced by the Institute for Scientific Information maintained by Clarivate Analytics, that provides a comprehensive citation search. It gives access to multiple databases that reference cross-disciplinary research, which allows for in-depth exploration of specialized sub-fields within an academic or scientific discipline. A citation index is built on the fact that citations in science serve as linkages between similar research items, lead to matching or related scientific literature, such as journal articles, conference proceedings, etc. In addition, literature which shows the greatest impact in a particular field, or more than one discipline, can be located through a citation index. For example, a paper's influence can be determined by linking to all the papers. In this way, current trends and emerging fields of research can be assessed. Eugene Garfield, the "father of citation indexing of academic literature," who launched the Science Citation Index, which in turn led to the Web of Science, wrote: Citations are the formal, explicit linkages between papers that have particular points in common.
A citation index is built around these linkages. It identifies the sources of the citations. Anyone conducting a literature search can find from one to dozens of additional papers on a subject just by knowing one, cited, and every paper, found provides a list of new citations with which to continue the search. The simplicity of citation indexing is one of its main strengths. Web of Science is described as a unifying research tool which enables the user to acquire and disseminate database information in a timely manner; this is accomplished because of the creation of a common vocabulary, called ontology, for varied search terms and varied data. Moreover, search terms generate related information across categories. Acceptable content for Web of Science is determined by an evaluation and selection process based on the following criteria: impact, timeliness, peer review, geographic representation. Web of Science employs various analysis capabilities. First, citation indexing is employed, enhanced by the capability to search for results across disciplines.
The influence, impact and methodology of an idea can be followed from its first instance, notice, or referral to the present day. This technology points to a deficiency with the keyword-only method of searching. Second, subtle trends and patterns relevant to the literature or research of interest, become apparent. Broad trends indicate significant topics of the day, as well as the history relevant to both the work at hand, particular areas of study. Third, trends can be graphically represented. Expanding the coverage of Web of Science, in November 2009 Thomson Reuters introduced Century of Social Sciences; this service contains files which trace social science research back to the beginning of the 20th century, Web of Science now has indexing coverage from the year 1900 to the present. As of 3 September 2014, the multidisciplinary coverage of the Web of Science encompasses over 50,000 scholarly books, 12,000 journals and 160,000 conference proceedings; the selection is made on the basis of impact evaluations and comprise open-access journals, spanning multiple academic disciplines.
The coverage includes: the sciences, social sciences and humanities, goes across disciplines. However, Web of Science does not index all journals. There is a positive correlation between Impact Factor and CiteScore. However, analysis by Elsevier has identified 216 journals from 70 publishers to be in the top 10 percent of the most-cited journals in their subject category based on the CiteScore while they did not have Impact Factor, it appears that Impact Factor does not provide a comprehensive and an unbiased coverage of high quality journals. Similar results can be observed by comparing Impact Factor with SCImago Journal Rank. Furthermore, as of September 3, 2014 the total file count of the Web of Science was 90 million records, which included over a billion cited references; this citation service on average indexes around 65 million items per year, it is described as the largest accessible citation database. Titles of foreign-language publications are translated into English and so cannot be found by searches in the original language.
The Web of Science Core Collection consists of six online databases: Science Citation Index Expanded covers more than 8,500 notable journals encompassing 150 disciplines. Coverage is from the year 1900 to the present day. Social Sciences Citation Index covers more than 3,000 journals in social science disciplines. Range of coverage is from the year 1900 to the present day. Arts & Humanities Citation Index covers more than 1,700 arts and humanities journals starting from 1975. In addition, 250 major scientific and social sciences journals are covered. Emerging Sources Citation Index covers over 5,000 journals in the sciences, social science, humanities. Book Citation Index covers more than 60,000 editorially selected books starting from 2005. Conference Proceedings Citation Index covers more than 160,000 conference titles in the Sciences starting from 1990 to the present day Since 2008, the Web of Science hosts a number of regional citation indices; the Chinese Science Citation Database, produced in partnership with the Chinese Academy of Sciences, was the first one in a language other than English.
It was followed in 2013 by the SciELO Citation Index, covering Brazil, Portugal, the Cari
In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems. Algorithms can perform calculation, data processing, automated reasoning, other tasks; as an effective method, an algorithm can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function. Starting from an initial state and initial input, the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states producing "output" and terminating at a final ending state; the transition from one state to the next is not deterministic. The concept of algorithm has existed for centuries. Greek mathematicians used algorithms in the sieve of Eratosthenes for finding prime numbers, the Euclidean algorithm for finding the greatest common divisor of two numbers; the word algorithm itself is derived from the 9th century mathematician Muḥammad ibn Mūsā al-Khwārizmī, Latinized Algoritmi.
A partial formalization of what would become the modern concept of algorithm began with attempts to solve the Entscheidungsproblem posed by David Hilbert in 1928. Formalizations were framed as attempts to define "effective calculability" or "effective method"; those formalizations included the Gödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's Formulation 1 of 1936, Alan Turing's Turing machines of 1936–37 and 1939. The word'algorithm' has its roots in Latinizing the name of Muhammad ibn Musa al-Khwarizmi in a first step to algorismus. Al-Khwārizmī was a Persian mathematician, astronomer and scholar in the House of Wisdom in Baghdad, whose name means'the native of Khwarazm', a region, part of Greater Iran and is now in Uzbekistan. About 825, al-Khwarizmi wrote an Arabic language treatise on the Hindu–Arabic numeral system, translated into Latin during the 12th century under the title Algoritmi de numero Indorum; this title means "Algoritmi on the numbers of the Indians", where "Algoritmi" was the translator's Latinization of Al-Khwarizmi's name.
Al-Khwarizmi was the most read mathematician in Europe in the late Middle Ages through another of his books, the Algebra. In late medieval Latin, English'algorism', the corruption of his name meant the "decimal number system". In the 15th century, under the influence of the Greek word ἀριθμός'number', the Latin word was altered to algorithmus, the corresponding English term'algorithm' is first attested in the 17th century. In English, it was first used in about 1230 and by Chaucer in 1391. English adopted the French term, but it wasn't until the late 19th century that "algorithm" took on the meaning that it has in modern English. Another early use of the word is from 1240, in a manual titled Carmen de Algorismo composed by Alexandre de Villedieu, it begins thus: Haec algorismus ars praesens dicitur, in qua / Talibus Indorum fruimur bis quinque figuris. Which translates as: Algorism is the art by which at present we use those Indian figures, which number two times five; the poem is a few hundred lines long and summarizes the art of calculating with the new style of Indian dice, or Talibus Indorum, or Hindu numerals.
An informal definition could be "a set of rules that defines a sequence of operations". Which would include all computer programs, including programs that do not perform numeric calculations. A program is only an algorithm if it stops eventually. A prototypical example of an algorithm is the Euclidean algorithm to determine the maximum common divisor of two integers. Boolos, Jeffrey & 1974, 1999 offer an informal meaning of the word in the following quotation: No human being can write fast enough, or long enough, or small enough† to list all members of an enumerably infinite set by writing out their names, one after another, in some notation, but humans can do something useful, in the case of certain enumerably infinite sets: They can give explicit instructions for determining the nth member of the set, for arbitrary finite n. Such instructions are to be given quite explicitly, in a form in which they could be followed by a computing machine, or by a human, capable of carrying out only elementary operations on symbols.
An "enumerably infinite set" is one whose elements can be put into one-to-one correspondence with the integers. Thus and Jeffrey are saying that an algorithm implies instructions for a process that "creates" output integers from an arbitrary "input" integer or integers that, in theory, can be arbitrarily large, thus an algorithm can be an algebraic equation such as y = m + n – two arbitrary "input variables" m and n that produce an output y. But various authors' attempts to define the notion indicate that the word implies much more than this, something on the order of: Precise instructions for a fast, efficient, "good" process that specifies the "moves" of "the computer" to find and process arbitrary input integers/symbols m and n, symbols + and =... and "effectively" produce, in a "reasonable" time, output-integer y at a specified place and in a specified format
An academic or scholarly journal is a periodical publication in which scholarship relating to a particular academic discipline is published. Academic journals serve as permanent and transparent forums for the presentation and discussion of research, they are peer-reviewed or refereed. Content takes the form of articles presenting original research, review articles, book reviews; the purpose of an academic journal, according to Henry Oldenburg, is to give researchers a venue to "impart their knowledge to one another, contribute what they can to the Grand design of improving natural knowledge, perfecting all Philosophical Arts, Sciences."The term academic journal applies to scholarly publications in all fields. Scientific journals and journals of the quantitative social sciences vary in form and function from journals of the humanities and qualitative social sciences; the first academic journal was Journal des sçavans, followed soon after by Philosophical Transactions of the Royal Society, Mémoires de l'Académie des Sciences.
The first peer-reviewed journal was Medical Essays and Observations. The idea of a published journal with the purpose of " people know what is happening in the Republic of Letters" was first conceived by Eudes de Mazerai in 1663. A publication titled Journal littéraire général was supposed to be published to fulfill that goal, but never was. Humanist scholar Denis de Sallo and printer Jean Cusson took Mazerai's idea, obtained a royal privilege from King Louis XIV on 8 August 1664 to establish the Journal des sçavans; the journal's first issue was published on 5 January 1665. It was aimed at people of letters, had four main objectives: review newly published major European books, publish the obituaries of famous people, report on discoveries in arts and science, report on the proceedings and censures of both secular and ecclesiastical courts, as well as those of Universities both in France and outside. Soon after, the Royal Society established Philosophical Transactions of the Royal Society in March 1665, the Académie des Sciences established the Mémoires de l'Académie des Sciences in 1666, which more focused on scientific communications.
By the end of the 18th century, nearly 500 such periodical had been published, the vast majority coming from Germany and England. Several of those publications however, in particular the German journals, tended to be short lived. A. J. Meadows has estimated the proliferation of journal to reach 10,000 journals in 1950, 71,000 in 1987. However, Michael Mabe warns that the estimates will vary depending on the definition of what counts as a scholarly publication, but that the growth rate has been "remarkably consistent over time", with an average rates of 3.46% per year from 1800 to 2003. In 1733, Medical Essays and Observations was established by the Medical Society of Edinburgh as the first peer-reviewed journal. Peer review was introduced as an attempt to increase the pertinence of submissions. Other important events in the history of academic journals include the establishment of Nature and Science, the establishment of Postmodern Culture in 1990 as the first online-only journal, the foundation of arXiv in 1991 for the dissemination of preprints to be discussed prior to publication in a journal, the establishment of PLOS One in 2006 as the first megajournal.
There are two kinds of article or paper submissions in academia: solicited, where an individual has been invited to submit work either through direct contact or through a general submissions call, unsolicited, where an individual submits a work for potential publication without directly being asked to do so. Upon receipt of a submitted article, editors at the journal determine whether to reject the submission outright or begin the process of peer review. In the latter case, the submission becomes subject to review by outside scholars of the editor's choosing who remain anonymous; the number of these peer reviewers varies according to each journal's editorial practice – no fewer than two, though sometimes three or more, experts in the subject matter of the article produce reports upon the content and other factors, which inform the editors' publication decisions. Though these reports are confidential, some journals and publishers practice public peer review; the editors either choose to reject the article, ask for a revision and resubmission, or accept the article for publication.
Accepted articles are subjected to further editing by journal editorial staff before they appear in print. The peer review can take from several weeks to several months. Review articles called "reviews of progress," are checks on the research published in journals; some journals are devoted to review articles, some contain a few in each issue, others do not publish review articles. Such reviews cover the research from the preceding year, some for longer or shorter terms; some journals are enumerative. Yet others are evaluative; some journals are published in series, each covering a complete subject field year, or covering specific fields through several years. Unlike original research article
Nature is a British multidisciplinary scientific journal, first published on 4 November 1869. It is one of the most recognizable scientific journals in the world, was ranked the world's most cited scientific journal by the Science Edition of the 2010 Journal Citation Reports and is ascribed an impact factor of 40.137, making it one of the world's top academic journals. It is one of the few remaining academic journals that publishes original research across a wide range of scientific fields. Research scientists are the primary audience for the journal, but summaries and accompanying articles are intended to make many of the most important papers understandable to scientists in other fields and the educated public. Towards the front of each issue are editorials and feature articles on issues of general interest to scientists, including current affairs, science funding, scientific ethics and research breakthroughs. There are sections on books and short science fiction stories; the remainder of the journal consists of research papers, which are dense and technical.
Because of strict limits on the length of papers the printed text is a summary of the work in question with many details relegated to accompanying supplementary material on the journal's website. There are many fields of research in which important new advances and original research are published as either articles or letters in Nature; the papers that have been published in this journal are internationally acclaimed for maintaining high research standards. Fewer than 8% of submitted papers are accepted for publication. In 2007 Nature received the Prince of Asturias Award for Humanity; the enormous progress in science and mathematics during the 19th century was recorded in journals written in German or French, as well as in English. Britain underwent enormous technological and industrial changes and advances in the latter half of the 19th century. In English the most respected scientific journals of this time were the refereed journals of the Royal Society, which had published many of the great works from Isaac Newton, Michael Faraday through to early works from Charles Darwin.
In addition, during this period, the number of popular science periodicals doubled from the 1850s to the 1860s. According to the editors of these popular science magazines, the publications were designed to serve as "organs of science", in essence, a means of connecting the public to the scientific world. Nature, first created in 1869, was not the first magazine of its kind in Britain. One journal to precede Nature was Recreative Science: A Record and Remembrancer of Intellectual Observation, created in 1859, began as a natural history magazine and progressed to include more physical observational science and technical subjects and less natural history; the journal's name changed from its original title to Intellectual Observer: A Review of Natural History, Microscopic Research, Recreative Science and later to the Student and Intellectual Observer of Science and Art. While Recreative Science had attempted to include more physical sciences such as astronomy and archaeology, the Intellectual Observer broadened itself further to include literature and art as well.
Similar to Recreative Science was the scientific journal Popular Science Review, created in 1862, which covered different fields of science by creating subsections titled "Scientific Summary" or "Quarterly Retrospect", with book reviews and commentary on the latest scientific works and publications. Two other journals produced in England prior to the development of Nature were the Quarterly Journal of Science and Scientific Opinion, established in 1864 and 1868, respectively; the journal most related to Nature in its editorship and format was The Reader, created in 1864. These similar journals all failed; the Popular Science Review survived longest, lasting 20 years and ending its publication in 1881. The Quarterly Journal, after undergoing a number of editorial changes, ceased publication in 1885; the Reader terminated in 1867, Scientific Opinion lasted a mere 2 years, until June 1870. Not long after the conclusion of The Reader, a former editor, Norman Lockyer, decided to create a new scientific journal titled Nature, taking its name from a line by William Wordsworth: "To the solid ground of nature trusts the Mind that builds for aye".
First owned and published by Alexander Macmillan, Nature was similar to its predecessors in its attempt to "provide cultivated readers with an accessible forum for reading about advances in scientific knowledge." Janet Browne has proposed that "far more than any other science journal of the period, Nature was conceived and raised to serve polemic purpose." Many of the early editions of Nature consisted of articles written by members of a group that called itself the X Club, a group of scientists known for having liberal and somewhat controversial scientific beliefs relative to the time period. Initiated by Thomas Henry Huxley, the group consisted of such important scientists as Joseph Dalton Hooker, Herbert Spencer, John Tyndall, along with another five scientists and mathematicians, it was in part its scientific liberality that made Nature a longer-lasti
In graph theory and network analysis, indicators of centrality identify the most important vertices within a graph. Applications include identifying the most influential person in a social network, key infrastructure nodes in the Internet or urban networks, super-spreaders of disease. Centrality concepts were first developed in social network analysis, many of the terms used to measure centrality reflect their sociological origin, they should not be confused with node influence metrics, which seek to quantify the influence of every node in the network. Centrality indices are answers to the question "What characterizes an important vertex?" The answer is given in terms of a real-valued function on the vertices of a graph, where the values produced are expected to provide a ranking which identifies the most important nodes. The word "importance" has a wide number of meanings, leading to many different definitions of centrality. Two categorization schemes have been proposed. "Importance" can transfer across the network.
This allows centralities to be classified by the type of flow they consider important. "Importance" can alternatively be conceived as involvement in the cohesiveness of the network. This allows centralities to be classified based on. Both of these approaches divide centralities in distinct categories. A further conclusion is that a centrality, appropriate for one category will "get it wrong" when applied to a different category; when centralities are categorized by their approach to cohesiveness, it becomes apparent that the majority of centralities inhabit one category. The count of the number of walks starting from a given vertex differs only in how walks are defined and counted. Restricting consideration to this group allows for a soft characterization which places centralities on a spectrum from walks of length one to infinite walks; the observation that many centralities share this familial relationships explains the high rank correlations between these indices. A network can be considered a description of the paths along.
This allows a characterization based on the type of flow and the type of path encoded by the centrality. A flow can be based on transfers, where each undivisible item goes from one node to another, like a package delivery which goes from the delivery site to the client's house. A second case is the serial duplication, where this is a replication of the item which goes to the next node, so both the source and the target have it. An example is the propagation of information through gossip, with the information being propagated in a private way and with both the source and the target nodes being informed at the end of the process; the last case is the parallel duplication, with the item being duplicated to several links at the same time, like a radio broadcast which provides the same information to many listeners at once. The type of path can be constrained to: Geodesics, trails, or walks. An alternative classification can be derived from; this again splits into two classes. Centralities are either Medial.
Radial centralities count walks. The degree and eigenvalue centralities are examples of radial centralities, counting the number of walks of length one or length infinity. Medial centralities count walks; the canonical example is Freeman's betweenness centrality, the number of shortest paths which pass through the given vertex. The counting can capture either the volume or the length of walks. Volume is the total number of walks of the given type; the three examples from the previous paragraph fall into this category. Length captures the distance from the given vertex to the remaining vertices in the graph. Freeman's closeness centrality, the total geodesic distance from a given vertex to all other vertices, is the best known example. Note that this classification is independent of the type of walk counted. Borgatti and Everett propose that this typology provides insight into how best to compare centrality measures. Centralities placed in the same box in this 2×2 classification are similar enough to make plausible alternatives.
Measures from different boxes, are categorically distinct. Any evaluation of relative fitness can only occur within the context of predetermining which category is more applicable, rendering the comparison moot; the characterization by walk structure shows that all centralities in wide use are radial-volume measures. These encode the belief that a vertex's centrality is a function of the centrality of the vertices it is associated with. Centralities distinguish themselves on. Bonacich showed that if association is defined in terms of walks a family of centralities can be defined based on the length of walk considered; the degree counts walks of length one, the eigenvalue centrality counts walks of length infinity. Alternative definitions of association are reasonable; the alpha centrality allows vertices to have an external source of influence. Estrada's subgraph centrality proposes only counting closed paths; the heart of such measures is the observation that powers of the graph's adjacency matrix gives the number of walks of length given by that power.
The matrix exponential is closely related to the number of walks of a given l