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38 relations: Algorithm, Angular resolution (graph drawing), Arc (geometry), Barnes–Hut simulation, Centrality, Connected component (graph theory), Convex position, Coulomb's law, Cytoscape, Electric charge, Euclidean distance, Genetic algorithm, Gephi, Global optimization, Graph (discrete mathematics), Graph drawing, Graphviz, Hooke's law, Limit of a sequence, Mathematical optimization, Maxima and minima, Mechanical equilibrium, Multidimensional scaling, N-body problem, N-body simulation, Online algorithm, Peter Eades, Planar graph, Polyhedral graph, Prefuse, Roberto Tamassia, Simulated annealing, Spline (mathematics), Spring (device), Stress majorization, Time complexity, Tulip (software), Tutte embedding.
Algorithm
In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.
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Angular resolution (graph drawing)
In graph drawing, the angular resolution of a drawing of a graph refers to the sharpest angle formed by any two edges that meet at a common vertex of the drawing.
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Arc (geometry)
In Euclidean geometry, an arc (symbol: ⌒) is a closed segment of a differentiable curve.
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Barnes–Hut simulation
The Barnes–Hut simulation (Josh Barnes and Piet Hut) is an approximation algorithm for performing an ''n''-body simulation.
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Centrality
In graph theory and network analysis, indicators of centrality identify the most important vertices within a graph.
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Connected component (graph theory)
In graph theory, a connected component (or just component) of an undirected graph is a subgraph in which any two vertices are connected to each other by paths, and which is connected to no additional vertices in the supergraph.
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Convex position
In discrete and computational geometry, a set of points in the Euclidean plane is said to be in convex position or convex independent if none of the points can be represented as a convex combination of the others.
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Coulomb's law
Coulomb's law, or Coulomb's inverse-square law, is a law of physics for quantifying the amount of force with which stationary electrically charged particles repel or attract each other.
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Cytoscape
Cytoscape is an open source bioinformatics software platform for visualizing molecular interaction networks and integrating with gene expression profiles and other state data.
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Electric charge
Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field.
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Euclidean distance
In mathematics, the Euclidean distance or Euclidean metric is the "ordinary" straight-line distance between two points in Euclidean space.
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Genetic algorithm
In computer science and operations research, a genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA).
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Gephi
Gephi is an open-source network analysis and visualization software package written in Java on the NetBeans platform.
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Global optimization
Global optimization is a branch of applied mathematics and numerical analysis that deals with the global optimization of a function or a set of functions according to some criteria.
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Graph (discrete mathematics)
In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".
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Graph drawing
Graph drawing is an area of mathematics and computer science combining methods from geometric graph theory and information visualization to derive two-dimensional depictions of graphs arising from applications such as social network analysis, cartography, linguistics, and bioinformatics.
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Graphviz
Graphviz (short for Graph Visualization Software) is a package of open-source tools initiated by AT&T Labs Research for drawing graphs specified in DOT language scripts.
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Hooke's law
Hooke's law is a principle of physics that states that the force needed to extend or compress a spring by some distance scales linearly with respect to that distance.
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Limit of a sequence
As the positive integer n becomes larger and larger, the value n\cdot \sin\bigg(\frac1\bigg) becomes arbitrarily close to 1.
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Mathematical optimization
In mathematics, computer science and operations research, mathematical optimization or mathematical programming, alternatively spelled optimisation, is the selection of a best element (with regard to some criterion) from some set of available alternatives.
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Maxima and minima
In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the local or relative extrema) or on the entire domain of a function (the global or absolute extrema).
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Mechanical equilibrium
In classical mechanics, a particle is in mechanical equilibrium if the net force on that particle is zero.
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Multidimensional scaling
Multidimensional scaling (MDS) is a means of visualizing the level of similarity of individual cases of a dataset.
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N-body problem
In physics, the -body problem is the problem of predicting the individual motions of a group of celestial objects interacting with each other gravitationally.
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N-body simulation
In physics and astronomy, an N-body simulation is a simulation of a dynamical system of particles, usually under the influence of physical forces, such as gravity (see ''n''-body problem).
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Online algorithm
In computer science, an online algorithm is one that can process its input piece-by-piece in a serial fashion, i.e., in the order that the input is fed to the algorithm, without having the entire input available from the start.
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Peter Eades
Peter D. Eades (born January 8, 1952) is an Australian computer scientist, a professor in the School of Information Technologies at the University of Sydney, known for his expertise in graph drawing.
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Planar graph
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints.
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Polyhedral graph
In geometric graph theory, a branch of mathematics, a polyhedral graph is the undirected graph formed from the vertices and edges of a convex polyhedron.
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Prefuse
Prefuse is a Java-based toolkit for building interactive information visualization applications.
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Roberto Tamassia
Roberto Tamassia is an Italian computer scientist, the Plastech Professor of Computer Science at Brown University, and served as the chair of the Brown Computer Science department from 2007 to 2014.
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Simulated annealing
Simulated annealing (SA) is a probabilistic technique for approximating the global optimum of a given function.
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Spline (mathematics)
In mathematics, a spline is a function defined piecewise by polynomials.
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Spring (device)
A spring is an elastic object that stores mechanical energy.
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Stress majorization
Stress majorization is an optimization strategy used in multidimensional scaling (MDS) where, for a set of n m-dimensional data items, a configuration X of n points in r(\sigma(X). Usually r is 2 or 3, i.e. the (n x r) matrix X lists points in 2- or 3-dimensional Euclidean space so that the result may be visualised (i.e. an MDS plot). The function \sigma is a cost or loss function that measures the squared differences between ideal (m-dimensional) distances and actual distances in r-dimensional space. It is defined as: where w_\ge 0 is a weight for the measurement between a pair of points (i,j), d_(X) is the euclidean distance between i and j and \delta_ is the ideal distance between the points (their separation) in the m-dimensional data space. Note that w_ can be used to specify a degree of confidence in the similarity between points (e.g. 0 can be specified if there is no information for a particular pair). A configuration X which minimizes \sigma(X) gives a plot in which points that are close together correspond to points that are also close together in the original m-dimensional data space. There are many ways that \sigma(X) could be minimized. For example, Kruskal recommended an iterative steepest descent approach. However, a significantly better (in terms of guarantees on, and rate of, convergence) method for minimizing stress was introduced by Jan de Leeuw.. De Leeuw's iterative majorization method at each step minimizes a simple convex function which both bounds \sigma from above and touches the surface of \sigma at a point Z, called the supporting point. In convex analysis such a function is called a majorizing function. This iterative majorization process is also referred to as the SMACOF algorithm ("Scaling by MAjorizing a COmplicated Function").
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Time complexity
In computer science, the time complexity is the computational complexity that describes the amount of time it takes to run an algorithm.
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Tulip (software)
Tulip is an information visualization framework dedicated to the analysis and visualization of relational data.
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Tutte embedding
In graph drawing and geometric graph theory, a Tutte embedding or barycentric embedding of a simple 3-vertex-connected planar graph is a crossing-free straight-line embedding with the properties that the outer face is a convex polygon and that each interior vertex is at the average (or barycenter) of its neighbors' positions.
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References
[1] https://en.wikipedia.org/wiki/Force-directed_graph_drawing
