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Topics referred to by the same term
A two-dimensional graph may refer to The graph of a function of one variable A planar graph A diagram in a plane This disambiguation page lists mathematics
Two-dimensional_graph
Topics referred to by the same term
A three-dimensional graph may refer to A graph (discrete mathematics), embedded into a three-dimensional space The graph of a function of two variables
Three-dimensional_graph
2D graphic with logarithmic scales on both axes
In science and engineering, a log–log graph or log–log plot is a two-dimensional graph of numerical data that uses logarithmic scales on both the horizontal
Log–log_plot
Barycentric plot on three variables
compositions is that three variables can be conveniently plotted in a two-dimensional graph. Ternary plots can also be used to create phase diagrams by outlining
Ternary_plot
Function specifying the behavior of a component in an electronic or control system
inputs. The transfer function of a two-port electronic circuit, such as an amplifier, might be a two-dimensional graph of the scalar voltage at the output
Transfer_function
Concentration of a vapor in contact with its liquid
concentrations when boiling at various temperatures can be shown as a two-dimensional graph called a boiling-point diagram. The mole fraction of component 1
Vapor–liquid_equilibrium
Natural number
294 is the number of planar biconnected graphs with 7 vertices. Biconnected graphs are two dimensional graphs with a given number of points and 294 is
294_(number)
Heuristic test for graph isomorphism
networks: a standard message-passing graph neural network can distinguish two graphs only if the one-dimensional Weisfeiler Leman (1-WL) test distinguishes
Weisfeiler Leman graph isomorphism test
Weisfeiler_Leman_graph_isomorphism_test
Mineral assemblage in metamorphic rocks
of what is formed in conditions corresponding to an area on the two dimensional graph of temperature vs. pressure (See diagram in Figure 1). Rocks which
Metamorphic_facies
Geometrical concept
non-empty intersection of a solid body in three-dimensional space with a plane, or the analog in higher-dimensional spaces. Cutting an object into slices creates
Cross_section_(geometry)
Schläfli graph is the edge graph of the 6-dimensional 221 polytope. The Gosset graph is the edge graph of the 7-dimensional 321 polytope. Some operations
Graph_of_a_polytope
Graphs formed by a hypercube's edges and vertices
In graph theory, the hypercube graph Qn is the edge graph of the n-dimensional hypercube, that is, it is the graph formed from the vertices and edges
Hypercube_graph
Graph of chess rook moves
graphs of complete bipartite graphs. The square rook's graphs constitute the two-dimensional Hamming graphs. Rook's graphs are highly symmetric, having
Rook's_graph
Distance-regular graph with 56 vertices
Gosset graph, named after Thorold Gosset, is a distance-regular graph with 56 vertices and valency 27. It is the 1-skeleton of the 7-dimensional 321 polytope
Gosset_graph
One of two different regular graphs with 16 vertices
dimension-5 folded cube graph (the 5-regular Clebsch graph) may be constructed by adding edges between opposite pairs of vertices in a 4-dimensional hypercube
Clebsch_graph
Number of vertices with unambiguous distances
In graph theory, the metric dimension of a graph G is the minimum cardinality of a subset S of vertices such that all other vertices are uniquely determined
Metric dimension (graph theory)
Metric_dimension_(graph_theory)
Graph of neutrons vs. protons in nuclides
A table or chart of nuclides is a two-dimensional graph of isotopes of the chemical elements, in which one axis represents the number of neutrons (symbol
Table_of_nuclides
Integer associated with a graph
particularly in graph theory, the dimension of a graph is the least integer n such that there exists a "classical representation" of the graph in the Euclidean
Dimension_(graph_theory)
Natural number
are included. Seventeen is the minimum number of vertices on a two-dimensional graph such that, if the edges are colored with three different colors
17_(number)
Physical simulation to visualize graphs
way. Their purpose is to position the nodes of a graph in two-dimensional or three-dimensional space so that all the edges are of more or less equal
Force-directed_graph_drawing
Representation of a mathematical function
pairs (x,y) –, the graph usually refers to the set of ordered triples (x,y,z) where f(x,y)=z. This is a subset of three-dimensional space; for a continuous
Graph_of_a_function
Graph that encodes local operations in mathematics
Among the connected flip graphs, one also finds the flip graphs of any finite 2-dimensional set of points. In higher dimensional Euclidean spaces, the situation
Flip_graph
Piece by Iannis Xenakis for string orchestra
is a four-dimensional phenomenon (three spatial dimensions and time), and Xenakis created the score by first creating a two-dimensional graph, necessitating
Pithoprakta
Set of unordered triples from a vertex set
the two-graph. A regular two-graph has the property that every pair of vertices lies in the same number of triples of the two-graph. Two-graphs have
Two-graph
crystallography, a periodic graph or crystal net is a three-dimensional periodic graph, i.e., a three-dimensional Euclidean graph whose vertices or nodes
Periodic graph (crystallography)
Periodic_graph_(crystallography)
Solid with six equal square faces
squares. It is a three-dimensional hypercube, a family of polytopes that also includes the two-dimensional square and four-dimensional tesseract. The cube
Cube
Geometric model of the planar projection of the physical universe
a plane is a flat two-dimensional surface that extends indefinitely. Euclidean planes often arise as subspaces of three-dimensional space ℝ3. A prototypical
Euclidean_plane
Graph of the vertices and edges of a demihypercube
In graph theory, the halved cube graph or half cube graph of dimension n is the vertex-edge graph of the demihypercube, formed by connecting pairs of vertices
Halved_cube_graph
Directed graph whose edges are labelled invertibly by elements of a group
cover of a graph), d-dimensional integer lattices ℤd (viewed as a group under vector addition, for defining periodic structures in d-dimensional Euclidean
Voltage_graph
Visualization of node-link graphs
and information visualization to derive two-dimensional (or, sometimes, three-dimensional) depictions of graphs arising from applications such as social
Graph_drawing
Class of simple graphs defined from vector spaces
Grassmann graph Jq(n, k) are the k-dimensional subspaces of an n-dimensional vector space over a finite field of order q; two vertices are adjacent when their
Grassmann_graph
Graph that can be embedded in the plane
generally, the genus of a graph is the minimum genus of a two-dimensional surface into which the graph may be embedded; planar graphs have genus zero and nonplanar
Planar_graph
Property of a charged particle beam
When the position and momentum for a single axis are plotted on a two dimensional graph, the average spread of the coordinates on this plot is the emittance
Beam_emittance
Graph of space and time in special relativity
diagrams are two-dimensional graphs that depict events as happening in a universe consisting of one space dimension and one time dimension. Unlike a regular
Spacetime_diagram
Graph in which every two vertices are adjacent
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
Complete_graph
Directed graph representing overlaps between sequences of symbols
In graph theory, an n-dimensional De Bruijn graph of m symbols is a directed graph representing overlaps between sequences of symbols. It has mn vertices
De_Bruijn_graph
Electrical engineering plot
axis against another knob or variable on another axis, producing a two-dimensional graph. This allows the test engineer to visually observe the operating
Shmoo_plot
purposes of the model, analysis can be made on a two-dimensional graph. Optimal choices represent the bundle of two goods; the first good and the composite. A
Composite_good
define higher-dimensional chains. In particular, C2 would be the free abelian group on the set of 2-dimensional objects. However, in a graph there are no
Graph_homology
Positive-definite integral set of repeated points with Abelian group-rank 24
is the following graph: Each point represents one of the 24 Niemeier lattices, and the lines joining them represent the 24 dimensional odd unimodular lattices
Niemeier_lattice
Property of a mathematical space
sphere. A two-dimensional Euclidean space is a two-dimensional space on the plane. The inside of a cube, a cylinder or a sphere is three-dimensional (3D) because
Dimension
Set of data elements in databases
represented as a table with two columns and three rows, or as a two-dimensional graph with three points. The table and graph representations are only equivalent
Table_(database)
Optimization problem
discretization of time. The two-dimensional graph of vertices of the form (x,y) is replaced by a three-dimensional graph of vertices of the form (x,y
Vehicle_routing_problem
Periodic spatial graph
Laves graph is an infinite and highly symmetric system of points and line segments in three-dimensional Euclidean space, forming a periodic graph. Three
Laves_graph
Embedding a graph in a topological space, often Euclidean
known that any finite graph can be embedded in 3-dimensional Euclidean space R 3 {\displaystyle \mathbb {R} ^{3}} . A planar graph is one that can be embedded
Graph_embedding
Graph representing faces of another graph
of planar graph duality include a version of duality for directed graphs, and duality for graphs embedded onto non-planar two-dimensional surfaces. These
Dual_graph
Problem of grouping into triples
mathematical discipline of graph theory, a 3-dimensional matching is a generalization of bipartite matching (also known as 2-dimensional matching) to 3-partite
3-dimensional_matching
Embedding of the circle in three dimensional Euclidean space
knot theory and has many relations to graph theory. A knot is an embedding of the circle (S1) into three-dimensional Euclidean space (R3), or the 3-sphere
Knot_(mathematics)
Formula that visually represents itself when graphed
paper on reliable two-dimensional computer graphing algorithms. This paper discusses methods related to the GrafEq formula-graphing program developed
Tupper's self-referential formula
Tupper's_self-referential_formula
Graph-theoretic description of polyhedra
undirected graphs formed by the edges and vertices of three-dimensional convex polyhedra: they are exactly the 3-vertex-connected planar graphs. That is
Steinitz's_theorem
Area of discrete mathematics
undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the
Graph_theory
Vertices connected in pairs by edges
In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a set of objects where some pairs of the objects are in some
Graph_(discrete_mathematics)
Geometry problem on grid points
problem can be used for two-dimensional graph drawing, one can use this three-dimensional solution to draw graphs in the three-dimensional grid. Here the non-collinearity
No-three-in-line_problem
Graph divided into two independent sets
In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets
Bipartite_graph
Geometric configuration of ten points and lines
Graphs associated with the Desargues configuration include the Desargues graph (its graph of point-line incidences) and the Petersen graph (its graph
Desargues_configuration
Geometric graph with unit edge lengths
particularly geometric graph theory, a unit distance graph is a graph formed from a collection of points in the Euclidean plane by connecting two points whenever
Unit_distance_graph
Cubic graph with 10 vertices and 15 edges
mathematical field of graph theory, the Petersen graph is an undirected graph with 10 vertices and 15 edges. It is a small graph that serves as a useful
Petersen_graph
Four-dimensional analogue of the cube
a tesseract or 4-cube is a four-dimensional hypercube, analogous to a two-dimensional square and a three-dimensional cube. Just as the perimeter of the
Tesseract
3-regular graph with 30 vertices and 45 edges
mathematical field of graph theory, the Tutte–Coxeter graph or Tutte eight-cage or Cremona–Richmond graph is a 3-regular graph with 30 vertices and 45
Tutte–Coxeter_graph
Visual representation of music
1987 by Kjell Gustafson, whose method represents a rhythm as a two-dimensional graph. Rhythmic notation during its early stages developed Eastern musical
Musical_notation
Topological structure in loop quantum gravity
possible configurations of spin foam.[how?] A spin network is a two-dimensional graph, together with labels on its vertices and edges which encode aspects
Spin_foam
Graph defined from a mathematical group
infinite group, and despite being embedded in a three-dimensional space, the Cayley graph has four-dimensional volume growth. The group G acts on itself by left
Cayley_graph
Mathematical graph relating to chess
4} knight's graph is the same as the four-dimensional hypercube graph. King's graph Queen's graph Rook's graph Bishop's graph Lattice graph Averbach, Bonnie;
Knight's_graph
16-regular graph with 27 vertices and 216 edges
vectors in the eight-dimensional representation described above. A graph is defined to be k-ultrahomogeneous if every isomorphism between two of its induced
Schläfli_graph
Abstract data type in computer science
science, a graph is an abstract data type that is meant to implement the undirected graph and directed graph concepts from the field of graph theory within
Graph_(abstract_data_type)
Graph with oriented edges
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
Directed_graph
Curve along which a 3D surface is at equal elevation
points of equal value to the state. It is a plane section of the three-dimensional graph of the function f ( x , y ) {\displaystyle f(x,y)} parallel to the
Contour_line
Undirected unit-distance graph requiring four colors
Pisanski (2011) to show the NP-hardness of testing whether a given graph has a two-dimensional unit distance representation; the proof uses a reduction from
Moser_spindle
Geometry problem on tiling by hypercubes
any tiling of n-dimensional Euclidean space by identical hypercubes, there are two hypercubes that share an entire (n − 1)-dimensional face with each other
Keller's_conjecture
Combinatorial representation of a graph on an orientable surface
fat graph, or a cyclic graph. More generally, an n-dimensional combinatorial map is a combinatorial representation of a graph on an n-dimensional orientable
Combinatorial_map
2D surface which extends indefinitely
point (zero dimensions), a line (one dimension) and three-dimensional space. When working exclusively in two-dimensional Euclidean space, the definite article
Plane_(mathematics)
Dimensionality reduction of graph-based semantic data objects [machine learning task]
learning, is a machine learning task of learning a low-dimensional representation of a knowledge graph's entities and relations while preserving their meaning
Knowledge_graph_embedding
In graph theory and theoretical computer science, the colour refinement algorithm also known as the naive vertex classification, or the 1-dimensional version
Colour_refinement_algorithm
Computational statistics technique
one dimension, one can perform a uniformly random sampling of the two-dimensional Cartesian graph, and keep the samples in the region under the graph of
Rejection_sampling
ordered pairs (x,y) such that y = f(x). This is the ordinary two-dimensional Cartesian graph studied in school algebra. Every complex number has both a
Tetraview
Mathematical measure for partial orders
comparability graphs of the partial orders of dimension two are exactly the permutation graphs, graphs that are both themselves comparability graphs and complementary
Order_dimension
infinite unit distance graph on all points of the Euclidean plane or of any higher-dimensional Euclidean space is a core. Every finite graph has a core, which
Core_(graph_theory)
Method of approximating the properties of a composite material
resistor network can be considered as a two-dimensional graph and the effective resistance can be modelled in terms of graph measures and geometrical properties
Effective medium approximations
Effective_medium_approximations
Family of graphs with 2n nodes and n(n-1) edges
In graph theory, a branch of mathematics, a crown graph on 2n vertices is an undirected graph with two sets of vertices {u1, u2, …, un} and {v1, v2, …
Crown_graph
Function describing the energy of a physical system in terms of certain parameters
surfaces are commonly shown as three-dimensional graphs, but they can also be represented by two-dimensional graphs, in which the advancement of the reaction
Potential_energy_surface
Archimedean solid with 32 faces
this property, including the four-dimensional 600-cell, the three-dimensional icosidodecahedron, and the two-dimensional decagon. (The icosidodecahedron
Icosidodecahedron
Mathematical abstraction of level sets
the Reeb graph can be not one-dimensional and even non-Hausdorff space. In fact, the compactness of the manifold is crucial: The Reeb graph of a smooth
Reeb_graph
Study of graphs defined by geometric means
Geometric graph theory in the broader sense is a large and amorphous subfield of graph theory, concerned with graphs defined by geometric means. In a stricter
Geometric_graph_theory
Sequence of edges which join a sequence of vertices on a given graph
In graph theory, a path in a graph is a finite or infinite sequence of edges which joins a sequence of vertices which, by most definitions, are all distinct
Path_(graph_theory)
Representation learning technique
representation learning technique that maps complex, high-dimensional data into a lower-dimensional vector space of numerical vectors. It also denotes the
Embedding_(machine_learning)
Type of topological space
loopless graph is represented by a regular 1-dimensional CW-complex. A closed 2-cell graph embedding on a surface is a regular 2-dimensional CW-complex
CW_complex
Theorem on triangulation graph colorings
induction on the dimension of a simplex. We apply the same reasoning, as in the two-dimensional case, to conclude that in a n-dimensional triangulation there
Sperner's_lemma
Graphs of d-dimensional polytopes are d-connected
theorem is a statement about the graph-theoretic structure of three-dimensional convex polyhedra and higher-dimensional convex polytopes. It states that
Balinski's_theorem
Crystalline materials consisting of a single layer of atoms
two-dimensional materials can be also expected below other two-dimensional materials, significantly influencing the properties of the two-dimensional
Single-layer_materials
Geometric graph connecting nearby points
the relative neighborhood graph (RNG) is an undirected graph defined on a set of points in the Euclidean plane by connecting two points p {\displaystyle
Relative_neighborhood_graph
Graph used in computational complexity theory and graph theory
number. Then the Frankl–Rödl graph FRγn is the graph on the 2n vertices of an n-dimensional unit hypercube [0,1]n in which two vertices are adjacent when
Frankl–Rödl_graph
Regular polytope dual to the hypercube in any number of dimensions
vertex-edge graph of an n-dimensional cross-polytope is the Turán graph T(2n, n) (also known as a cocktail party graph ). In 1 dimension the cross-polytope
Cross-polytope
Graph often embedded in the Klein bottle
conjecture on the number of colors needed when a two-dimensional surface is partitioned into cells by a graph embedding. The Heawood conjecture implied that
Franklin_graph
Basic concept of graph theory
concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into two or more
Connectivity_(graph_theory)
{\displaystyle d} -dimensional normed vector space is a property of graphs which states that any embedding, or drawing, of the graph in some high dimension d ′ {\displaystyle
Graph_flattenability
Screening method
_{i}\right)^{2}}}} . These two measures need to be read together (e.g. on a two-dimensional graph) in order to rank input factors in order
Elementary_effects_method
Mathematical problem
color the plane so that no two points at unit distance are the same color? More unsolved problems in mathematics In geometric graph theory, the Hadwiger–Nelson
Hadwiger–Nelson_problem
Type of crystal structure
diamond cubic involves the removal of some of the edges from a three-dimensional grid graph. In this coordinatization, which has a distorted geometry from the
Diamond_cubic
Graph made from vertices and edges of a convex polyhedron
purely graph-theoretic terms, the polyhedral graphs are the 3-vertex-connected, planar graphs. The analogue concept for polytopes of general dimension are
Polyhedral_graph
Projection of data onto lower-dimensional manifolds
is a sample on a two-dimensional manifold in 1024-dimensional space (a Hamming space). The intrinsic dimensionality is two, because two variables (rotation
Nonlinear dimensionality reduction
Nonlinear_dimensionality_reduction
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TWO DIMENSIONAL-GRAPH
TWO DIMENSIONAL-GRAPH
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