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Graph Theory
In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph theory), vertices'' (also called ''nodes'' or ''points'') which are connected by ''Glossary of graph theory terms#edge, edges'' (also called ''arcs'', ''links'' or ''lines''). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics. Definitions Definitions in graph theory vary. The following are some of the more basic ways of defining graphs and related mathematical structures. Graph In one restricted but very common sense of the term, a graph is an ordered pair G=(V,E) comprising: * V, a Set (mathematics), set of vertices (also called nodes or points); * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Example Of Simple Undirected Graph 3
Example may refer to: * ''exempli gratia'' (e.g.), usually read out in English as "for example" * .example, reserved as a domain name that may not be installed as a top-level domain of the Internet ** example.com, example.net, example.org, and example.edu: second-level domain names reserved for use in documentation as examples * HMS Example (P165), HMS ''Example'' (P165), an Archer-class patrol and training vessel of the Royal Navy Arts * ''The Example'', a 1634 play by James Shirley * The Example (comics), ''The Example'' (comics), a 2009 graphic novel by Tom Taylor and Colin Wilson * Example (musician), the British dance musician Elliot John Gleave (born 1982) * Example (album), ''Example'' (album), a 1995 album by American rock band For Squirrels See also * Exemplar (other), a prototype or model which others can use to understand a topic better * Exemplum, medieval collections of short stories to be told in sermons * Eixample, a district of Barcelona with di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pseudograph
In mathematics, and more specifically in graph theory, a multigraph is a graph which is permitted to have multiple edges (also called ''parallel edges''), that is, edges that have the same end nodes. Thus two vertices may be connected by more than one edge. There are 2 distinct notions of multiple edges: * ''Edges without own identity'': The identity of an edge is defined solely by the two nodes it connects. In this case, the term "multiple edges" means that the same edge can occur several times between these two nodes. * ''Edges with own identity'': Edges are primitive entities just like nodes. When multiple edges connect two nodes, these are different edges. A multigraph is different from a hypergraph, which is a graph in which an edge can connect any number of nodes, not just two. For some authors, the terms ''pseudograph'' and ''multigraph'' are synonymous. For others, a pseudograph is a multigraph that is permitted to have loops. Undirected multigraph (edges withou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Algorithms
An algorithm is fundamentally a set of rules or defined procedures that is typically designed and used to solve a specific problem or a broad set of problems. Broadly, algorithms define process(es), sets of rules, or methodologies that are to be followed in calculations, data processing, data mining, pattern recognition, automated reasoning or other problem-solving operations. With the increasing automation of services, more and more decisions are being made by algorithms. Some general examples are; risk assessments, anticipatory policing, and pattern recognition technology. The following is a list of well-known algorithms. Automated planning Combinatorial algorithms General combinatorial algorithms * Brent's algorithm: finds a cycle in function value iterations using only two iterators * Floyd's cycle-finding algorithm: finds a cycle in function value iterations * Gale–Shapley algorithm: solves the stable matching problem * Pseudorandom number generators (uniformly dis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use Conditional (computer programming), conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning). In contrast, a Heuristic (computer science), heuristic is an approach to solving problems without well-defined correct or optimal results.David A. Grossman, Ophir Frieder, ''Information Retrieval: Algorithms and Heuristics'', 2nd edition, 2004, For example, although social media recommender systems are commonly called "algorithms", they actually rely on heuristics as there is no truly "correct" recommendation. As an e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperlink
In computing, a hyperlink, or simply a link, is a digital reference providing direct access to Data (computing), data by a user (computing), user's point and click, clicking or touchscreen, 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 content from Wikipedia or Google Search, many words and terms in the text are hyperlinked to definitions of those terms. Hyperlinks are often used to implement reference mechanism (engineering), mechanisms such as tables of contents, footnotes, bibliographies, index (publishing), indexes, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Website
A website (also written as a web site) is any web page whose content is identified by a common domain name and is published on at least one web server. Websites are typically dedicated to a particular topic or purpose, such as news, education, commerce, entertainment, or social media. Hyperlinking between web pages guides the navigation of the site, which often starts with a home page. The most-visited sites are Google, YouTube, and Facebook. All publicly-accessible websites collectively constitute the World Wide Web. There are also private websites that can only be accessed on a private network, such as a company's internal website for its employees. Users can access websites on a range of devices, including desktops, laptops, tablets, and smartphones. The app used on these devices is called a web browser. Background The World Wide Web (WWW) was created in 1989 by the British CERN computer scientist Tim Berners-Lee. On 30 April 1993, CERN announced that the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cybernetics
Cybernetics is the transdisciplinary study of circular causal processes such as feedback and recursion, where the effects of a system's actions (its outputs) return as inputs to that system, influencing subsequent action. It is concerned with general principles that are relevant across multiple contexts, including in engineering, ecological, economic, biological, cognitive and social systems and also in practical activities such as designing, learning, and managing. Cybernetics' transdisciplinary character has meant that it intersects with a number of other fields, leading to it having both wide influence and diverse interpretations. The field is named after an example of circular causal feedback—that of steering a ship (the ancient Greek κυβερνήτης (''kybernḗtēs'') refers to the person who steers a ship). In steering a ship, the position of the rudder is adjusted in continual response to the effect it is observed as having, forming a feedback loop throu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Network Science
Network science is an academic field which studies complex networks such as telecommunication networks, computer networks, biological networks, Cognitive network, cognitive and semantic networks, and social networks, considering distinct elements or actors represented by ''nodes'' (or ''vertices'') and the connections between the elements or actors as ''links'' (or ''edges''). The field draws on theories and methods including graph theory from mathematics, statistical mechanics from physics, data mining and information visualization from computer science, inferential statistics, inferential modeling from statistics, and social structure from sociology. The United States National Research Council defines network science as "the study of network representations of physical, biological, and social phenomena leading to predictive models of these phenomena." Background and history The study of networks has emerged in diverse disciplines as a means of analyzing complex relational ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wikipedia Multilingual Network Graph July 2013
Wikipedia is a free online encyclopedia that is written and maintained by a community of volunteers, known as Wikipedians, through open collaboration and the wiki software MediaWiki. Founded by Jimmy Wales and Larry Sanger in 2001, Wikipedia has been hosted since 2003 by the Wikimedia Foundation, an American nonprofit organization funded mainly by donations from readers. Wikipedia is the largest and most-read reference work in history. Initially available only in English, Wikipedia exists in over 340 languages. The English Wikipedia, with over million articles, remains the largest of the editions, which together comprise more than articles and attract more than 1.5 billion unique device visits and 13 million edits per month (about 5edits per second on average) . , over 25% of Wikipedia's traffic comes from the United States, while Japan, the United Kingdom, Germany and Russia each account for around 5%. Wikipedia has been praised for enabling th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quiver (mathematics)
In mathematics, especially representation theory, a quiver is another name for a multidigraph; that is, a directed graph where Loop (graph theory), loops and multiple arrows between two vertex (graph theory), vertices are allowed. Quivers are commonly used in representation theory: a representation of a quiver assigns a vector space to each vertex of the quiver and a linear map to each arrow . In category theory, a quiver can be understood to be the underlying structure of a category (mathematics), category, but without composition or a designation of identity morphisms. That is, there is a forgetful functor from (the category of categories) to (the category of multidigraphs). Its left adjoint is a free functor which, from a quiver, makes the corresponding free category. Definition A quiver consists of: * The set of vertices of * The set of edges of * Two functions: giving the ''start'' or ''source'' of the edge, and another function, givin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiple Edges
In graph theory, multiple edges (also called parallel edges or a multi-edge), are, in an undirected graph, two or more edges that are incident to the same two vertices, or in a directed graph, two or more edges with both the same tail vertex and the same head vertex. A simple graph has no multiple edges and no loops. Depending on the context, a graph may be defined so as to either allow or disallow the presence of multiple edges (often in concert with allowing or disallowing loops): *Where graphs are defined so as to ''allow'' multiple edges and loops, a graph without loops or multiple edges is often distinguished from other graphs by calling it a ''simple graph.'' *Where graphs are defined so as to ''disallow'' multiple edges and loops, a multigraph or a pseudograph is often defined to mean a "graph" which ''can'' have multiple edges. Multiple edges are, for example, useful in the consideration of electrical networks, from a graph theoretical point of view. Additional ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tuple
In mathematics, a tuple is a finite sequence or ''ordered list'' of numbers or, more generally, mathematical objects, which are called the ''elements'' of the tuple. An -tuple is a tuple of elements, where is a non-negative integer. There is only one 0-tuple, called the ''empty tuple''. A 1-tuple and a 2-tuple are commonly called a singleton and an ordered pair, respectively. The term ''"infinite tuple"'' is occasionally used for ''"infinite sequences"''. Tuples are usually written by listing the elements within parentheses "" and separated by commas; for example, denotes a 5-tuple. Other types of brackets are sometimes used, although they may have a different meaning. An -tuple can be formally defined as the image of a function that has the set of the first natural numbers as its domain. Tuples may be also defined from ordered pairs by a recurrence starting from an ordered pair; indeed, an -tuple can be identified with the ordered pair of its first elements and its t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
