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Friendship Paradox
The friendship paradox is the phenomenon first observed by the sociologist Scott L. Feld in 1991 that most people have fewer friends than their friends have, on average. It can be explained as a form of sampling bias in which people with more friends are more likely to be in one's own friend group. In other words, one is less likely to be friends with someone who has very few friends. In contradiction to this, most people believe that they have more friends than their friends have. The same observation can be applied more generally to social networks defined by other relations than friendship: for instance, most people's sexual partners have had (on the average) a greater number of sexual partners than they have. The friendship paradox is an example of how network structure can significantly distort an individual's local observations. Mathematical explanation In spite of its apparently paradoxical nature, the phenomenon is real, and can be explained as a consequence of the gene ...
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Moreno Sociogram 2nd Grade
Moreno may refer to: Places Argentina *Moreno (Buenos Aires Metro), a station on Line C of the Buenos Aires Metro *Moreno, Buenos Aires, a city in Buenos Aires Province, Argentina *Moreno Department, a depatnent of Santiago del Estero Province, Argentina *Moreno Partido, a division of the Buenos Aires Province, Argentina Elsewhere *Moreno, California (other) *Moreno, Pernambuco, Brazil, a city *Moreno Rock, a rock in Antarctica * Point Moreno, a promontory on Laurie Island in the South Orkney Islands People with the name Lists of people with the name * Moreno (given name) *Moreno (surname) People with the nickname or professional name * Moreno (footballer, born 1948), Daniel Euclides Moreno, Brazilian football forward *Moreno (Portuguese footballer) (born 1981), Portuguese football defensive midfielder *Moreno (footballerc, born 1983), Moreno Aoas Vidal, Brazilian football leftback *Moreno (Spanish footballer) (born 1986), Spanish football defender *Moreno (singer) (bor ...
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Complete Graph
In the mathematical field of graph theory, a complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique edge. A complete digraph is a directed graph in which every pair of distinct vertices is connected by a pair of unique edges (one in each direction). Graph theory itself is typically dated as beginning with Leonhard Euler's 1736 work on the Seven Bridges of Königsberg. However, drawings of complete graphs, with their vertices placed on the points of a regular polygon, had already appeared in the 13th century, in the work of Ramon Llull. Such a drawing is sometimes referred to as a mystic rose. Properties The complete graph on vertices is denoted by . Some sources claim that the letter in this notation stands for the German word , but the German name for a complete graph, , does not contain the letter , and other sources state that the notation honors the contributions of Kazimierz Kuratowski to graph theory. has edges (a ...
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Social Networks
A social network is a social structure made up of a set of social actors (such as individuals or organizations), sets of dyadic ties, and other social interactions between actors. The social network perspective provides a set of methods for analyzing the structure of whole social entities as well as a variety of theories explaining the patterns observed in these structures. The study of these structures uses social network analysis to identify local and global patterns, locate influential entities, and examine network dynamics. Social networks and the analysis of them is an inherently interdisciplinary academic field which emerged from social psychology, sociology, statistics, and graph theory. Georg Simmel authored early structural theories in sociology emphasizing the dynamics of triads and "web of group affiliations". Jacob Moreno is credited with developing the first sociograms in the 1930s to study interpersonal relationships. These approaches were mathematically formalize ...
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Statistical Paradoxes
Statistics (from German: ''Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments.Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', Oxford University Press. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An expe ...
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Self-evaluation Maintenance Theory
Self-evaluation maintenance (SEM) concerns discrepancies between two people in a relationship. The theory posits an individual will maintain as well as enhance their self-esteem via a social comparison to another individual. Self-evaluation refers to the self-perceived social ranking one has towards themselves. It is the continuous process of determining personal growth and progress, which can be raised or lowered by the behavior of others. Abraham Tesser created the self-evaluation maintenance theory in 1988. The self-evaluation maintenance model assumes two things: that a person will try to maintain or increase their own self-evaluation, and self-evaluation is influenced by relationships with others. A person's self-evaluation (which is similar to self-esteem) may be raised when a close other performs well. For example, a sibling scores the winning goal in an important game. Self-evaluation will increase because that person is sharing his/her success. The closer the psychological r ...
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Second Neighborhood Problem
In mathematics, the second neighborhood problem is an unsolved problem about oriented graphs posed by Paul Seymour. Intuitively, it suggests that in a social network described by such a graph, someone will have at least as many friends-of-friends as friends. The problem is also known as the second neighborhood conjecture or Seymour’s distance two conjecture. Statement An oriented graph is a finite directed graph obtained from a simple undirected graph by assigning an orientation to each edge. Equivalently, it is a directed graph that has no self-loops, no parallel edges, and no two-edge cycles. The first neighborhood of a vertex v (also called its open neighborhood) consists of all vertices at distance one from v, and the second neighborhood of v consists of all vertices at distance two from v. These two neighborhoods form disjoint sets, neither of which contains v itself. In 1990, Paul Seymour conjectured that, in every oriented graph, there always exists at least one vertex v ...
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The Slate Group
The Slate Group, legally The Slate Group, LLC, is an American online publishing entity established in June 2008 by Graham Holdings Company. Among the publications overseen by The Slate Group are ''Slate'' and '' ForeignPolicy.com''. The creation of The Slate Group was announced by Donald Graham, the chairman and CEO of The Washington Post Company, in a press release on June 4, 2008. Its mission was stated as developing and managing a family of web-only magazines. The release also announced that Slate Group was expected to work closely with Washingtonpost.Newsweek Interactive in the areas of advertising sales, technology and marketing services. In 2014, The Slate Group had around 121 employees and reported more than 25 million unique visitors and more than 120 million page views per month on average.Graham Holdings2014 Annual Report(availablon GHCO.com Through a share in the French company E2J2 SAS and other support, The Slate Group is involved in the French-language websites ''S ...
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Slate Magazine
''Slate'' is an online magazine that covers current affairs, politics, and culture in the United States. It was created in 1996 by former '' New Republic'' editor Michael Kinsley, initially under the ownership of Microsoft as part of MSN. In 2004, it was purchased by The Washington Post Company (later renamed the Graham Holdings Company), and since 2008 has been managed by The Slate Group, an online publishing entity created by Graham Holdings. ''Slate'' is based in New York City, with an additional office in Washington, D.C. ''Slate'', which is updated throughout the day, covers politics, arts and culture, sports, and news. According to its former editor-in-chief Julia Turner, the magazine is "not fundamentally a breaking news source", but rather aimed at helping readers to "analyze and understand and interpret the world" with witty and entertaining writing. As of mid-2015, it publishes about 1,500 stories per month. A French version, ''slate.fr'', was launched in February 20 ...
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Heavy-tailed Distribution
In probability theory, heavy-tailed distributions are probability distributions whose tails are not exponentially bounded: that is, they have heavier tails than the exponential distribution. In many applications it is the right tail of the distribution that is of interest, but a distribution may have a heavy left tail, or both tails may be heavy. There are three important subclasses of heavy-tailed distributions: the fat-tailed distributions, the long-tailed distributions and the subexponential distributions. In practice, all commonly used heavy-tailed distributions belong to the subexponential class. There is still some discrepancy over the use of the term heavy-tailed. There are two other definitions in use. Some authors use the term to refer to those distributions which do not have all their power moments finite; and some others to those distributions that do not have a finite variance. The definition given in this article is the most general in use, and includes all dist ...
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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 k^\boldsymbol 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
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Power Law
In statistics, a power law is a Function (mathematics), functional relationship between two quantities, where a Relative change and difference, 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 Exponentiation, 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 ...
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Centrality
In graph theory and network analysis, indicators of centrality assign numbers or rankings to nodes within a graph corresponding to their network position. Applications include identifying the most influential person(s) in a social network, key infrastructure nodes in the Internet or urban networks, super-spreaders of disease, and brain networks. Centrality concepts were first developed in social network analysis, and many of the terms used to measure centrality reflect their sociological origin.Newman, M.E.J. 2010. ''Networks: An Introduction.'' Oxford, UK: Oxford University Press. Definition and characterization of centrality indices 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 diffe ...
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