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Webgraph
The webgraph describes the directed links between pages of the World Wide Web. A graph, in general, consists of several vertices, some pairs connected by edges. In a directed graph, edges are directed lines or arcs. The webgraph is a directed graph, whose vertices correspond to the pages of the WWW, and a directed edge connects page X to page Y if there exists a hyperlink on page X, referring to page Y. Properties * The degree distribution of the webgraph strongly differs from the degree distribution of the classical random graph model, the Erdős–Rényi model: in the Erdős–Rényi model, there are very few large degree nodes, relative to the webgraph's degree distribution. The precise distribution is unclear, however: it is relatively well described by a lognormal distribution, as well as the Barabási–Albert model for power laws. * The webgraph is an example of a scale-free network. Applications The webgraph is used for: * computing the PageRank of the WWW-pages; * co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
World Wide Web
The World Wide Web (WWW), commonly known as the Web, is an information system enabling documents and other web resources to be accessed over the Internet. Documents and downloadable media are made available to the network through web servers and can be accessed by programs such as web browsers. Servers and resources on the World Wide Web are identified and located through character strings called uniform resource locators (URLs). The original and still very common document type is a web page formatted in Hypertext Markup Language (HTML). This markup language supports plain text, images, embedded video and audio contents, and scripts (short programs) that implement complex user interaction. The HTML language also supports hyperlinks (embedded URLs) which provide immediate access to other web resources. Web navigation, or web surfing, is the common practice of following such hyperlinks across multiple websites. Web applications are web pages that function as application s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scale-free Network
A scale-free network is a network whose degree distribution follows a power law, at least asymptotically. That is, the fraction ''P''(''k'') of nodes in the network having ''k'' connections to other nodes goes for large values of ''k'' as : P(k) \ \sim \ k^\boldsymbol where \gamma is a parameter whose value is typically in the range 2<\gamma<3 (wherein the second moment () of is infinite but the first moment is finite), although occasionally it may lie outside these bounds. Many networks have been reported to be scale-free, although statistical analysis has refuted many of these claims and seriously questioned others. Additionally, some have argued that simply knowing that a degree-distribution is [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PageRank
PageRank (PR) is an algorithm used by Google Search to rank web pages in their search engine results. It is named after both the term "web page" and co-founder Larry Page. PageRank is a way of measuring the importance of website pages. According to Google: Currently, PageRank is not the only algorithm used by Google to order search results, but it is the first algorithm that was used by the company, and it is the best known. As of September 24, 2019, PageRank and all associated patents are expired. Description 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 PR(E). A PageRank results f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power Laws
In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities: one quantity varies as a power of another. For instance, considering the area of a square in terms of the length of its side, if the length is doubled, the area is multiplied by a factor of four. Empirical examples The distributions of a wide variety of physical, biological, and man-made phenomena approximately follow a power law over a wide range of magnitudes: these include the sizes of craters on the moon and of solar flares, the foraging pattern of various species, the sizes of activity patterns of neuronal populations, the frequencies of words in most languages, frequencies of family names, the species richness in clades of organisms, the sizes of power outages, volcanic eruptions, human judgments of stimulus intensity and many other quantit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperlink
In computing, a hyperlink, or simply a link, is a digital reference to data that the user can follow or be guided by clicking or tapping. A hyperlink points to a whole document or to a specific element within a document. Hypertext is text with hyperlinks. The text that is linked from is known as anchor text. A software system that is used for viewing and creating hypertext is a ''hypertext system'', and to create a hyperlink is ''to hyperlink'' (or simply ''to link''). A user following hyperlinks is said to ''navigate'' or ''browse'' the hypertext. The document containing a hyperlink is known as its source document. For example, in an online reference work such as Wikipedia or Google, many words and terms in the text are hyperlinked to definitions of those terms. Hyperlinks are often used to implement reference mechanisms such as tables of contents, footnotes, bibliographies, indexes, letters, and glossaries. In some hypertext, hyperlinks can be bidirectional: they can be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Degree Distribution
In the study of graphs and networks, the degree of a node in a network is the number of connections it has to other nodes and the degree distribution is the probability distribution of these degrees over the whole network. Definition The degree of a node in a network (sometimes referred to incorrectly as the connectivity) is the number of connections or edges the node has to other nodes. If a network is directed, meaning that edges point in one direction from one node to another node, then nodes have two different degrees, the in-degree, which is the number of incoming edges, and the out-degree, which is the number of outgoing edges. The degree distribution ''P''(''k'') of a network is then defined to be the fraction of nodes in the network with degree ''k''. Thus if there are ''n'' nodes in total in a network and ''n''''k'' of them have degree ''k'', we have P(k) = \frac. The same information is also sometimes presented in the form of a ''cumulative degree distribution'', the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erdős–Rényi Model
In the mathematical field of graph theory, the Erdős–Rényi model is either of two closely related models for generating random graphs or the evolution of a random network. They are named after Hungarian mathematicians Paul Erdős and Alfréd Rényi, who first introduced one of the models in 1959, while Edgar Gilbert introduced the other model contemporaneously and independently of Erdős and Rényi. In the model of Erdős and Rényi, all graphs on a fixed vertex set with a fixed number of edges are equally likely; in the model introduced by Gilbert, also called the Erdős–Rényi–Gilbert model, each edge has a fixed probability of being present or absent, independently of the other edges. These models can be used in the probabilistic method to prove the existence of graphs satisfying various properties, or to provide a rigorous definition of what it means for a property to hold for almost all graphs. Definition There are two closely related variants of the Erdős–R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lognormal
In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable is log-normally distributed, then has a normal distribution. Equivalently, if has a normal distribution, then the exponential function of , , has a log-normal distribution. A random variable which is log-normally distributed takes only positive real values. It is a convenient and useful model for measurements in exact and engineering sciences, as well as medicine, economics and other topics (e.g., energies, concentrations, lengths, prices of financial instruments, and other metrics). The distribution is occasionally referred to as the Galton distribution or Galton's distribution, after Francis Galton. The log-normal distribution has also been associated with other names, such as McAlister, Gibrat and Cobb–Douglas. A log-normal process is the statistical realization of the multipl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Barabási–Albert Model
The Barabási–Albert (BA) model is an algorithm for generating random scale-free network, scale-free complex network, networks using a preferential attachment mechanism. Several natural and human-made systems, including the Internet, the World Wide Web, citation analysis, citation networks, and some social networks are thought to be approximately scale-free and certainly contain few nodes (called hubs) with unusually high degree as compared to the other nodes of the network. The BA model tries to explain the existence of such nodes in real networks. The algorithm is named for its inventors Albert-László Barabási and Réka Albert. Concepts Many observed networks (at least approximately) fall into the class of scale-free networks, meaning that they have power law, power-law (or scale-free) degree distributions, while random graph models such as the Erdős–Rényi model, Erdős–Rényi (ER) model and the Watts and Strogatz model, Watts–Strogatz (WS) model do not exhibit pow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph (discrete Mathematics)
In discrete mathematics, and more specifically in graph theory, a graph is a structure amounting to a Set (mathematics), set of objects in which some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called ''Vertex (graph theory), vertices'' (also called ''nodes'' or ''points'') and each of the related pairs of vertices is called an ''edge'' (also called ''link'' or ''line''). Typically, a graph is depicted in diagrammatic form as a set of dots or circles for the vertices, joined by lines or curves for the edges. Graphs are one of the objects of study in discrete mathematics. The edges may be directed or undirected. For example, if the vertices represent people at a party, and there is an edge between two people if they shake hands, then this graph is undirected because any person ''A'' can shake hands with a person ''B'' only if ''B'' also shakes hands with ''A''. In contrast, if an edge from a person ''A'' to a person ''B'' m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Directed Graph
In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is made up of a set of vertices connected by directed edges, often called arcs. Definition In formal terms, a directed graph is an ordered pair where * ''V'' is a set whose elements are called '' vertices'', ''nodes'', or ''points''; * ''A'' is a set of ordered pairs of vertices, called ''arcs'', ''directed edges'' (sometimes simply ''edges'' with the corresponding set named ''E'' instead of ''A''), ''arrows'', or ''directed lines''. It differs from an ordinary or undirected graph, in that the latter is defined in terms of unordered pairs of vertices, which are usually called ''edges'', ''links'' or ''lines''. The aforementioned definition does not allow a directed graph to have multiple arrows with the same source and target nodes, but some authors consider a broader definition that allows directed graphs to have such multiple arcs (namely, they allow the arc set to be a m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sergei Brin
Sergey Mikhailovich Brin (russian: link=no, Сергей Михайлович Брин; born August 21, 1973) is an American business magnate A business magnate, also known as a tycoon, is a person who has achieved immense wealth through the ownership of multiple lines of enterprise. The term characteristically refers to a powerful entrepreneur or investor who controls, through perso ..., computer scientist, and internet entrepreneur, who co-founded Google with Larry Page. Brin was the president of Google's parent company, Alphabet Inc., until stepping down from the role on December 3, 2019. He and Page remain at Alphabet as co-founders, Controlling interest, controlling shareholders, board members, and employees. As of November 2022, Brin is the Bloomberg Billionaires Index, 12th-richest person in the world, with an estimated net worth of $78.0 billion. Brin immigrated to the United States with his family from the Soviet Union at the age of six. He earned his bachelor's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
