Betweenness (other)
Betweenness is a noun derived from the proposition between. It may refer to: * The ternary relation of intermediacy or betweenness, a feature of ordered geometry. * Betweenness problem - an algorithmic problem. The input is a collection of ordered triples of items; the task is to decide whether there is a single total order such that such that, for each of the given triples, the middle item in the triple appears in the output somewhere between the other two items. * Betweenness centrality - a measure of centrality in a graph, based on shortest paths. The betweenness centrality of a vertex is the number of shortest paths that pass through the vertex. * Metric betweenness - given a metric ''d'', a point ''y'' is said to be ''between'' ''x'' and ''z'' if all three points are distinct, and d(x,y)+d(y,z)=d(x,z). See convex metric space. See also * Between (other) * In Between (other) In Between may refer to: Film and television * ''In Between'', a 1991 film feat ...
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Ordered Geometry
Ordered geometry is a form of geometry featuring the concept of intermediacy (or "betweenness") but, like projective geometry, omitting the basic notion of measurement. Ordered geometry is a fundamental geometry forming a common framework for affine, Euclidean, absolute, and hyperbolic geometry (but not for projective geometry). History Moritz Pasch first defined a geometry without reference to measurement in 1882. His axioms were improved upon by Peano (1889), Hilbert (1899), and Veblen (1904). Euclid anticipated Pasch's approach in definition 4 of ''The Elements'': "a straight line is a line which lies evenly with the points on itself". Primitive concepts The only primitive notions in ordered geometry are points ''A'', ''B'', ''C'', ... and the ternary relation of intermediacy 'ABC''which can be read as "''B'' is between ''A'' and ''C''". Definitions The ''segment'' ''AB'' is the set of points ''P'' such that 'APB'' The ''interval'' ''AB'' is the segment ''AB'' and it ...
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Betweenness Problem
Betweenness is an algorithmic problem in order theory about ordering a collection of items subject to constraints that some items must be placed between others.. It has applications in bioinformatics. and was shown to be NP-complete by . Problem statement The input to a betweenness problem is a collection of ordered triples of items. The items listed in these triples should be placed into a total order, with the property that for each of the given triples, the middle item in the triple appears in the output somewhere between the other two items. The items of each triple are not required to be consecutive in the output. Examples As an example, the collection of input triples :(2,1,3), (3,4,5), (1,4,5), (2,4,1), (5,2,3) is satisfied by the output ordering :3, 1, 4, 2, 5 but not by :3, 1, 2, 4, 5. In the first of these output orderings, for all five of the input triples, the middle item of the triple appears between the other two items However, for the second output ordering, item ...
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Betweenness Centrality
In graph theory, betweenness centrality is a measure of centrality in a graph based on shortest paths. For every pair of vertices in a connected graph, there exists at least one shortest path between the vertices, that is, there exists at least one path such that either the number of edges that the path passes through (for unweighted graphs) or the sum of the weights of the edges (for weighted graphs) is minimized. Betweenness centrality was devised as a general measure of centrality: it applies to a wide range of problems in network theory, including problems related to social networks, biology, transport and scientific cooperation. Although earlier authors have intuitively described centrality as based on betweenness, gave the first formal definition of betweenness centrality. Betweenness centrality finds wide application in network theory; it represents the degree to which nodes stand between each other. For example, in a telecommunications network, a node with higher b ...
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Convex Metric Space
In mathematics, convex metric spaces are, intuitively, metric spaces with the property any "segment" joining two points in that space has other points in it besides the endpoints. Formally, consider a metric space (''X'', ''d'') and let ''x'' and ''y'' be two points in ''X''. A point ''z'' in ''X'' is said to be ''between'' ''x'' and ''y'' if all three points are distinct, and : d(x, z)+d(z, y)=d(x, y),\, that is, the triangle inequality becomes an equality. A convex metric space is a metric space (''X'', ''d'') such that, for any two distinct points ''x'' and ''y'' in ''X'', there exists a third point ''z'' in ''X'' lying between ''x'' and ''y''. Metric convexity: * does not imply convexity in the usual sense for subsets of Euclidean space (see the example of the rational numbers) * nor does it imply path-connectedness (see the example of the rational numbers) * nor does it imply geodesic convexity for Riemannian manifolds (consider, for example, the Euclidean plan ...
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Between (other)
Between is a preposition. It may also refer to: Arts and entertainment * ''Between'' (Frankmusik album), a 2013 album by Frankmusik * "Between", a song by Jerry Cantrell from ''Boggy Depot'' * ''Between'' (TV series), a Canadian science fiction-drama television and web series * ''Between'' (三明治女孩的逆襲), a 2018 Taiwanese television series * ''Between'', a 2008 video game designed by Jason Rohrer * ''The Between'', a 1995 novel by Tananarive Due Other uses * Between, Georgia, an American town See also * In Between (other) * Betweenness (other) Betweenness is a noun derived from the proposition between. It may refer to: * The ternary relation of intermediacy or betweenness, a feature of ordered geometry. * Betweenness problem - an algorithmic problem. The input is a collection of ordere ...