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Look up Graph, graph, or -graph in Wiktionary, the free dictionary. Wikimedia Commons has media related to Graphs. Graph may refer to: Graph (discrete...

computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context...

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...

The Graph is an open-source, decentralized protocol that powers the indexing and querying of blockchain data. It enables developers to build scalable...

In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it...

A graph database (GDB) is a database that uses graph structures for semantic queries with nodes, edges, and properties to represent and store data. A key...

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...

Flow graph may refer to: Flow or rooted graph (graph theory), a graph in which a vertex has been distinguished as the root Control-flow graph (computer...

knowledge graph is a knowledge base that uses a graph-structured data model or topology to represent and operate on data. Knowledge graphs are often used...

Appendix:Glossary of graph theory in Wiktionary, the free dictionary. This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes...

knowledge graph in Wiktionary, the free dictionary. A knowledge graph is a knowledge base that uses a graph-structured data model. Knowledge Graph may also...

Graph neural networks (GNNs) are artificial neural networks designed for tasks whose inputs are graphs. Because graphs usually do not have a canonical...

constraint graphs and hypergraphs are used to represent relations among constraints in a constraint satisfaction problem. A constraint graph is a special...

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...

In graph theory, a tree is an undirected graph in which every pair of distinct vertices is connected by exactly one path, or equivalently, a connected...

precedence graph, also named conflict graph and serializability graph, is used in the context of concurrency control in databases. It is the directed graph representing...

In graph theory, an undirected graph H is called a minor of the graph G if H can be formed from G by deleting edges and vertices and by contracting edges...

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...

computing, a graph state is a special type of multi-qubit state that can be represented by a graph. Each qubit is represented by a vertex of the graph, and there...

bridgeless graph has a cycle-continuous mapping to the Petersen graph. More unsolved problems in mathematics In the mathematical field of graph theory, the...

A bar chart or bar graph is a chart or graph that presents categorical data with rectangular bars with heights or lengths proportional to the values that...

In mathematics, the graph of a function f {\displaystyle f} is the set of ordered pairs ( x , y ) {\displaystyle (x,y)} , where f ( x ) = y . {\displaystyle...

In structure mining, a graph kernel is a kernel function that computes an inner product on graphs. Graph kernels can be intuitively understood as functions...

In graph theory, graph coloring is a methodic assignment of labels traditionally called "colors" to elements of a graph. The assignment is subject to certain...

especially in the fields of universal algebra and graph theory, a graph algebra is a way of giving a directed graph an algebraic structure. It was introduced...

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...

In the mathematical field of graph theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix, or discrete Laplacian...

In graph theory, a perfect graph is a graph in which the chromatic number equals the size of the maximum clique, both in the graph itself and in every...

In mathematics, and, in particular, in graph theory, a rooted graph is a graph in which one vertex has been distinguished as the root. Both directed and...

Graph matching is the problem of finding a similarity between graphs. Graphs are commonly used to encode structural information in many fields, including...

combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, mathematical logic, number theory, set theory, Ramsey...

Graph paper, coordinate paper, grid paper, or squared paper is writing paper that is printed with fine lines making up a regular grid. It is available...

Grapher is a computer program bundled with macOS since version 10.4 that is able to create 2D and 3D graphs from simple and complex equations. It includes...

In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges...

In mathematics, spectral graph theory is the study of the properties of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors...

In the structure of written articles in journalism, the nut graph or nut graf (short for "nutshell paragraph") is a paragraph following the lede, or opening...

In algebraic topology and graph theory, graph homology describes the homology groups of a graph, where the graph is considered as a topological space....

Under Graph is a Japanese band that was formed in 1997. Vocals/Guitar: Naoto Matohara (真戸原 直人, Matohara Naoto) Birthdate: July 27, 1977 Equipment: Gibson...

In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether...

In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group, is a graph that encodes the abstract...

mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that...

Volpert graph, Vol'pert graph or Wolpert graph may refer to: Volpert nomogram, a diagram better known as "Smith chart" coinvented by Russian engineer Amiel...

In graph theory, the Kneser graph K(n, k) (alternatively KGn,k) is the graph whose vertices correspond to the k-element subsets of a set of n elements...

In graph theory, an expander graph is a sparse graph that has strong connectivity properties, quantified using vertex, edge or spectral expansion. Expander...

Graph literacy is the ability to understand information that presented graphically, which are including general knowledge about how to extract information...

In statistics, a misleading graph, also known as a distorted graph, is a graph that misrepresents data, constituting a misuse of statistics and with the...

geometric group theory, a graph of groups is an object consisting of a collection of groups indexed by the vertices and edges of a graph, together with a family...

specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set...

In graph theory, the degree (or valency) of a vertex of a graph is the number of edges that are incident to the vertex; in a multigraph, a loop contributes...

social graph is a graph that represents social relations between entities. It is a model or representation of a social network. The social graph has been...

Graph drawing is an area of mathematics and computer science combining methods from geometric graph theory and information visualization to derive two-dimensional...

In graph theory, a cycle in a graph is a non-empty trail in which only the first and last vertices are equal. A directed cycle in a directed graph is...

mathematics, graph enumeration describes a class of combinatorial enumeration problems in which one must count undirected or directed graphs of certain...

In graph theory, the hypercube graph Q n {\displaystyle Q_{n}} is the edge graph of the n {\displaystyle n} -dimensional hypercube, that is, it is the...

(graph theory), a cycle in a graph Forest (graph theory), an undirected graph with no cycles Biconnected graph, an undirected graph in which every edge belongs...

computer science, graph transformation, or graph rewriting, concerns the technique of creating a new graph out of an original graph algorithmically. It...

In the mathematical field of graph theory, the Rado graph, Erdős–Rényi graph, or random graph is a countably infinite graph that can be constructed (with...

mathematical field of graph theory, the butterfly graph (also called the bowtie graph and the hourglass graph) is a planar, undirected graph with 5 vertices...

mathematics, computer science and digital electronics, a dependency graph is a directed graph representing dependencies of several objects towards each other...

In graph theory, an Eulerian trail (or Eulerian path) is a trail in a finite graph that visits every edge exactly once (allowing for revisiting vertices)...

In mathematics, the graph Fourier transform is a mathematical transform which eigendecomposes the Laplacian matrix of a graph into eigenvalues and eigenvectors...

In graph theory, a cycle graph or circular graph is a graph that consists of a single cycle, or in other words, some number of vertices (at least 3, if...

In graph theory, a tolerance graph is an undirected graph in which every vertex can be represented by a closed interval and a real number called its tolerance...

In the mathematical field of graph theory, a complete bipartite graph or biclique is a special kind of bipartite graph where every vertex of the first...

In graph theory, a lattice graph, mesh graph, or grid graph is a graph whose drawing, embedded in some Euclidean space ⁠ R n {\displaystyle \mathbb {R}...

mathematical discipline of graph theory, the dual graph of a planar graph G is a graph that has a vertex for each face of G. The dual graph has an edge for each...

a graph polynomial is a graph invariant whose value is a polynomial. Invariants of this type are studied in algebraic graph theory. Important graph polynomials...

In mathematics, a graph partition is the reduction of a graph to a smaller graph by partitioning its set of nodes into mutually exclusive groups. Edges...

In graph theory, trapezoid graphs are intersection graphs of trapezoids between two horizontal lines. They are a class of co-comparability graphs that...

A bond graph is a graphical representation of the energy flows though and between physical dynamical systems including those in the electrical, mechanical...

In the mathematical discipline of graph theory, a matching or independent edge set in an undirected graph is a set of edges without common vertices. In...

In graph theory, an intersection graph is a graph that represents the pattern of intersections of a family of sets. Any graph can be represented as an...

Acyclic graph may refer to: Directed acyclic graph, a directed graph without any directed cycles Forest (graph theory), an undirected acyclic graph Polytree...

mathematical field of graph theory, the ladder graph Ln is a planar, undirected graph with 2n vertices and 3n − 2 edges. The ladder graph can be obtained as...

In the mathematical field of graph theory, the Grötzsch graph is a triangle-free graph with 11 vertices, 20 edges, chromatic number 4, and crossing number...

In graph theory, a wheel graph is a graph formed by connecting a single universal vertex to all vertices of a cycle. A wheel graph with n vertices can...

2-graph may refer to one of the following: Two-graph, a graph-like combinatorial structure 2-regular graph, in graph theory This disambiguation page lists...

A call graph (also known as a call multigraph) is a control-flow graph, which represents calling relationships between subroutines in a computer program...

A signal-flow graph or signal-flowgraph (SFG), invented by Claude Shannon, but often called a Mason graph after Samuel Jefferson Mason who coined the...

GQL (Graph Query Language) is a standardized query language for property graphs first described in ISO/IEC 39075, released in April 2024 by ISO/IEC. The...

computer science, graph traversal (also known as graph search) refers to the process of visiting (checking and/or updating) each vertex in a graph. Such traversals...

Franklin graph Frucht graph Goldner–Harary graph Golomb graph Grötzsch graph Harries graph Harries–Wong graph Herschel graph Hoffman graph Hofman Graph H(12...

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 morphism may refer to: Graph homomorphism, in graph theory, a homomorphism between graphs Graph morphism, in algebraic geometry, a type of morphism...

mathematical field of graph theory, the diamond graph is a planar, undirected graph with 4 vertices and 5 edges. It consists of a complete graph ⁠ K 4 {\displaystyle...

mathematics In graph theory, a factor of a graph G is a spanning subgraph, i.e., a subgraph that has the same vertex set as G. A k-factor of a graph is a spanning...

In graph theory, a rook's graph is an undirected graph that represents all legal moves of the rook chess piece on a chessboard. Each vertex of a rook's...

In graph theory, a clique (/ˈkliːk/ or /ˈklɪk/) is a subset of vertices of an undirected graph such that every two distinct vertices in the clique are...

Chemical graph theory is the topology branch of mathematical chemistry which applies graph theory to mathematical modelling of chemical phenomena. The...

A scene graph is a hierarchical data structure commonly used by vector-based graphics editing applications and modern computer games, which cascades the...

the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly...

theory, the Schreier coset graph is a graph associated with a group G, a generating set of G, and a subgroup of G. The Schreier graph encodes the abstract structure...

A factor graph is a bipartite graph representing the factorization of a function. In probability theory and its applications, factor graphs are used to...

In graph theory, Graph equations are equations in which the unknowns are graphs. One of the central questions of graph theory concerns the notion of isomorphism...

The M22 graph, also called the Mesner graph or Witt graph, is the unique strongly regular graph with parameters (77, 16, 0, 4). It is constructed from...

Primal graph may refer to: Primal graph (hypergraphs) of a hypergraph A primal graph may be the planar graph from which a dual graph is formed Primal...

mathematical field of graph theory, the Wagner graph is a 3-regular graph with 8 vertices and 12 edges. It is the 8-vertex Möbius ladder graph. As a Möbius ladder...

The 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...

In the mathematical field of graph theory, Tietze's graph is an undirected cubic graph with 12 vertices and 18 edges. It is named after Heinrich Franz...

the mathematical fields of graph theory and finite model theory, the logic of graphs deals with formal specifications of graph properties using sentences...

of graph theory, a cubic graph is a graph in which all vertices have degree three. In other words, a cubic graph is a 3-regular graph. Cubic graphs are...

In graph theory, a circle graph is the intersection graph of a chord diagram. That is, it is an undirected graph whose vertices can be associated with...

In mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability...

field of graph theory, the triangle graph is a planar undirected graph with 3 vertices and 3 edges, in the form of a triangle. The triangle graph is also...

A property graph, labeled property graph, or attributed graph is a data model of various graph-oriented databases, where pairs of entities are associated...

In the area of graph theory in mathematics, a signed graph is a graph in which each edge has a positive or negative sign. A signed graph is balanced if...

In graph theory, an isomorphism of graphs G and H is a bijection between the vertex sets of G and H f : V ( G ) → V ( H ) {\displaystyle f\colon V(G)\to...

In the mathematical discipline of graph theory, a graph C is a covering graph of another graph G if there is a covering map from the vertex set of C to...

mathematical field of graph theory, the term "null graph" may refer either to the order-zero graph, or alternatively, to any edgeless graph (the latter is sometimes...

mathematics, the closed graph theorem may refer to one of several basic results characterizing continuous functions in terms of their graphs. Each gives conditions...

In topological graph theory, a 1-planar graph is a graph that can be drawn in the Euclidean plane in such a way that each edge has at most one crossing...

Open graph may refer to: A confused version of the Closed graph property The Open Graph Protocol This disambiguation page lists articles associated with...

A Sparse graph code is a code which is represented by a sparse graph. Any linear code can be represented as a graph, where there are two sets of nodes...

graphs are a way of modeling a system of tasks to be scheduled and timing constraints that must be respected by the schedule. They are mixed graphs,...

graph, but it is generally used in topological graph theory as a concise way to specify another graph called the derived graph of the voltage graph....

graph from an initial one by a complex change, such as: transpose graph; complement graph; line graph; graph minor; graph rewriting; power of graph;...

In graph theory, a division of mathematics, a median graph is an undirected graph in which every three vertices a {\displaystyle a} , b {\displaystyle...

In mathematics, a dense graph is a graph in which the number of edges is close to the maximal number of edges (where every pair of vertices is connected...

graph theory, a graph product is a binary operation on graphs. Specifically, it is an operation that takes two graphs G1 and G2 and produces a graph H...

Graph pebbling is a mathematical game played on a graph with zero or more pebbles on each of its vertices. 'Game play' is composed of a series of pebbling...

bipartite graphs. It was discovered independently, also in 1931, by Jenő Egerváry in the more general case of weighted graphs. A vertex cover in a graph is a...

discipline of graph theory, a graph labeling is the assignment of labels, traditionally represented by integers, to edges and/or vertices of a graph. Formally...

crystal Periodic graph (geometry), a Euclidean graph preserved under a lattice of translations Periodic graph (graph theory), a graph that is periodic...

In the mathematical field of graph theory, a graph homomorphism is a mapping between two graphs that respects their structure. More concretely, it is a...

In graph theory, a fractional isomorphism of graphs whose adjacency matrices are denoted A and B is a doubly stochastic matrix D such that DA = BD. If...

the mathematical field of graph theory, the friendship graph (or Dutch windmill graph or n-fan) Fn is a planar, undirected graph with 2n + 1 vertices and...

In graph theory, a mixed graph G = (V, E, A) is a graph consisting of a set of vertices V, a set of (undirected) edges E, and a set of directed edges (or...

mathematical field of graph theory, the Heawood graph is an undirected graph with 14 vertices and 21 edges, named after Percy John Heawood. The graph is cubic, and...

Elephant Curve, also known as the Lakner-Milanovic graph or the global growth incidence curve, is a graph that illustrates the unequal distribution of income...

Laves graph is an infinite and highly symmetric system of points and line segments in three-dimensional Euclidean space, forming a periodic graph. Three...

In mathematics, the Coates graph or Coates flow graph, named after C.L. Coates, is a graph associated with the Coates' method for the solution of a system...

field of graph theory, the windmill graph Wd(k,n) is an undirected graph constructed for k ≥ 2 and n ≥ 2 by joining n copies of the complete graph Kk at...

Sierpiński graphs (or Sierpiński networks) are a family of graphs defined by two parameters n {\displaystyle n} and k {\displaystyle k} , denoted S ( n...

In the mathematical area of graph theory, a chordal graph is one in which all cycles of four or more vertices have a chord, which is an edge that is not...

In the mathematical field of graph theory, the Chang graphs are three 12-regular undirected graphs, each with 28 vertices and 168 edges. They are strongly...

In polytope theory, the edge graph (also known as vertex-edge graph or just graph) of a polytope is a combinatorial graph whose vertices and edges correspond...

In the mathematical field of graph theory, an automorphism of a graph is a form of symmetry in which the graph is mapped onto itself while preserving...

In graph theory, a branch of mathematics, an indifference graph is an undirected graph constructed by assigning a real number to each vertex and connecting...

Skip graphs are a kind of distributed data structure based on skip lists. They were invented in 2003 by James Aspnes and Gauri Shah. A nearly identical...

In chemical graph theory and in mathematical chemistry, a molecular graph or chemical graph is a representation of the structural formula of a chemical...

mathematical field of graph theory, the Franklin graph is a 3-regular graph with 12 vertices and 18 edges. The Franklin graph is named after Philip Franklin...

Hamming graphs are a special class of graphs named after Richard Hamming and used in several branches of mathematics (graph theory) and computer science...

In the mathematical field of graph theory, the complement or inverse of a graph G is a graph H on the same vertices such that two distinct vertices are...

graph theory, the Chvátal graph is an undirected graph with 12 vertices and 24 edges, discovered by Václav Chvátal in 1970. It is the smallest graph that...

mathematics graph theory a process graph or P-graph is a directed bipartite graph used in workflow modeling. With a process graph, the vertices of the graph are...

In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency. A regular...

An interest graph is a digital portrayal of an individual's specific interests. Its perceived utility and value stem from the premise that a person's...

In graph theory, the Golomb graph is a polyhedral graph with 10 vertices and 18 edges. It is named after Solomon W. Golomb, who constructed it (with a...

A Euclidean graph (a graph embedded in some Euclidean space) is periodic if there exists a basis of that Euclidean space whose corresponding translations...

mathematics and physics, a quantum graph is a linear, network-shaped structure of vertices connected on edges (i.e., a graph) in which each edge is given a...

computational geometry, the Theta graph, or Θ {\displaystyle \Theta } -graph, is a type of geometric spanner similar to a Yao graph. The basic method of construction...

Bivariegated graph Cage (graph theory) Cayley graph Circle graph Clique graph Cograph Common graph Complement of a graph Complete graph Cubic graph Cycle graph De...

In mathematics, a topological graph is a representation of a graph in the plane, where the vertices of the graph are represented by distinct points and...

In graph theory, a quotient graph Q of a graph G is a graph whose vertices are blocks of a partition of the vertices of G and where block B is adjacent...

In mathematics, the commuting graph of a semigroup, or in particular of a group, is an undirected graph in which the vertices are elements of the semigroup...

In the mathematical field of graph theory, the pancake graph Pn or n-pancake graph is a graph whose vertices are the permutations of n symbols from 1 to...

discipline of graph theory, the (m,n)-lollipop graph is a special type of graph consisting of a complete graph (clique) on m vertices and a path graph on n vertices...

field of graph theory, the Pappus graph is a bipartite, 3-regular, undirected graph with 18 vertices and 27 edges, formed as the Levi graph of the Pappus...

Bounded-parameter graphs Graphs of bounded treewidth Graphs of bounded genus (Planar graphs are graphs of genus 0.) Graphs of bounded degree Graphs with bounded...

Does a Moore graph with girth 5 and degree 57 exist? More unsolved problems in mathematics In graph theory, a Moore graph is a regular graph whose girth...

mathematics, Johnson graphs are a special class of undirected graphs defined from systems of sets. The vertices of the Johnson graph J ( n , k ) {\displaystyle...

In topology, a branch of mathematics, a graph is a topological space which arises from a usual graph G = ( E , V ) {\displaystyle G=(E,V)} by replacing...

In graph theory, the Holt graph or Doyle graph is the smallest half-transitive graph, that is, the smallest example of a vertex-transitive and edge-transitive...

In topological graph theory, an embedding (also spelled imbedding) of a graph G {\displaystyle G} on a surface Σ {\displaystyle \Sigma } is a representation...

In combinatorial mathematics, a Levi graph or incidence graph is a bipartite graph associated with an incidence structure. From a collection of points...

mathematical field of graph theory, the Shrikhande graph is a graph discovered by S. S. Shrikhande in 1959. It is a strongly regular graph with 16 vertices...

visibility graph is a graph of intervisible locations, typically for a set of points and obstacles in the Euclidean plane. Each node in the graph represents...

of graph theory, the odd graphs are a family of symmetric graphs defined from certain set systems. They include and generalize the Petersen graph. The...

In graph theory, a component of an undirected graph is a connected subgraph that is not part of any larger connected subgraph. The components of any graph...

A bullet graph is a variation of a bar graph developed by Stephen Few. Seemingly inspired by the traditional thermometer charts and progress bars found...

mathematical field of graph theory, the Folkman graph is a 4-regular graph with 20 vertices and 40 edges. It is a regular bipartite graph with symmetries taking...

In geometric graph theory, a penny graph is a contact graph of unit circles. It is formed from a collection of unit circles that do not cross each other...

analysis, the closed graph theorem is a result connecting the continuity of a linear operator to a topological property of their graph. Precisely, the theorem...

In mathematics and social science, a collaboration graph is a graph modeling some social network where the vertices represent participants of that network...

In graph theory, a branch of mathematics, the Herschel graph is a bipartite undirected graph with 11 vertices and 18 edges. It is a polyhedral graph (the...

In graph theory, a circulant graph is an undirected graph acted on by a cyclic group of symmetries which takes any vertex to any other vertex. It is sometimes...

In the mathematical field of graph theory, the Robertson graph or (4,5)-cage, is a 4-regular undirected graph with 19 vertices and 38 edges named after...

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...

In graph theory, a bridge, isthmus, cut-edge, or cut arc is an edge of a graph whose deletion increases the graph's number of connected components. Equivalently...

In graph theory, a branch of combinatorial mathematics, a block graph or clique tree is a type of undirected graph in which every biconnected component...

(circular) or a cartesian coordinate (rectangular) graph, and either a line graph or a bar graph. In polar form, the months of the year are marked around...

In graph theory, a strongly regular graph (SRG) is a regular graph G = (V, E) with v vertices and degree k such that for some given integers λ , μ ≥ 0...

drawing a graph with vertices connected with an edge in a plane. Such a graph is called the cubical graph, a special case of the hypercube graph. The cube...

In graph theory, a graph property or graph invariant is a property of graphs that depends only on the abstract structure, not on graph representations...

objects are referred to as object graphs, after the mathematical objects called graphs studied in graph theory. An object graph is a view of an object system...

In computer science, a control-flow graph (CFG) is a representation, using graph notation, of all paths that might be traversed through a function during...

In the mathematical field of graph theory, the Dyck graph is a 3-regular graph with 32 vertices and 48 edges, named after Walther von Dyck. It is Hamiltonian...

Graph cut may refer to: Cut (graph theory), in mathematics Graph cut optimization Graph cuts in computer vision This disambiguation page lists articles...

In the mathematical field of graph theory, the Klein graphs are two different but related regular graphs, each with 84 edges. Each can be embedded in...

In graph theory, a knight's graph, or a knight's tour graph, is a graph that represents all legal moves of the knight chess piece on a chessboard. Each...

In the mathematical field of graph theory, the Dürer graph is an undirected graph with 12 vertices and 18 edges. It is named after Albrecht Dürer, whose...

In the mathematics of Sudoku, the Sudoku graph is an undirected graph whose vertices represent the cells of a (blank) Sudoku puzzle and whose edges represent...

mathematics, a queen's graph is an undirected graph that represents all legal moves of the queen—a chess piece—on a chessboard. In the graph, each vertex represents...

Borel graph theorem is generalization of the closed graph theorem that was proven by L. Schwartz. The Borel graph theorem shows that the closed graph theorem...

statistics, econometrics, epidemiology, genetics and related disciplines, causal graphs (also known as path diagrams, causal Bayesian networks or DAGs) are probabilistic...

In graph theory, a branch of mathematics, the kth power Gk of an undirected graph G is another graph that has the same set of vertices, but in which two...

In graph theory, a branch of mathematics, a split graph is a graph in which the vertices can be partitioned into a clique and an independent set. Split...

In graph theory, a branch of mathematics, a cluster graph is a graph formed from the disjoint union of complete graphs. Equivalently, a graph is a cluster...

A graph reduction machine is a special-purpose computer built to perform combinator calculations by graph reduction. Examples include the SKIM ("S-K-I...

"clique graph" may refer to: Complete graph, a graph in which every two vertices are adjacent Clique (graph theory), a complete subgraph Clique graph, the...

In graph-theoretic mathematics, a biregular graph or semiregular bipartite graph is a bipartite graph G = ( U , V , E ) {\displaystyle G=(U,V,E)} for which...

In computer science, graph reduction implements an efficient version of non-strict evaluation, an evaluation strategy where the arguments to a function...

In information theory, the graph entropy is a measure of the information rate achievable by communicating symbols over a channel in which certain pairs...

In mathematics, a fibration of graphs, or graph fibration, is a homomorphism of directed graphs that satisfies a unique lifting property analogous to that...

mathematics, the energy of a graph is the sum of the absolute values of the eigenvalues of the adjacency matrix of the graph. This quantity is studied in...

TigerGraph is a private company headquartered in Redwood City, California. It provides graph database and graph analytics software. TigerGraph was founded...

field of graph theory, an Archimedean graph is a graph that forms the skeleton of one of the Archimedean solids. There are 13 Archimedean graphs, and all...

In graph theory, the Games graph is the largest known locally linear strongly regular graph. Its parameters as a strongly regular graph are (729,112,1...

Paley graphs form an infinite family of conference graphs, which yield an infinite family of symmetric conference matrices. Paley graphs allow graph-theoretic...

Evolutionary graph theory is an area of research lying at the intersection of graph theory, probability theory, and mathematical biology. Evolutionary graph theory...

spectral graph theory, a Ramanujan graph is a regular graph whose spectral gap is almost as large as possible (see extremal graph theory). Such graphs are...

In the mathematical field of graph theory, the Nauru graph is a symmetric, bipartite, cubic graph with 24 vertices and 36 edges. It was named by David...

GraphBLAS (/ˈɡræfˌblɑːz/ ) is an API specification that defines standard building blocks for graph algorithms in the language of linear algebra. GraphBLAS...

topological graph theory is a branch of graph theory. It studies the embedding of graphs in surfaces, spatial embeddings of graphs, and graphs as topological...

In graph theory, a branch of mathematics, a half graph is a special type of bipartite graph. These graphs are called the half graphs because they have...

Layered graph drawing or hierarchical graph drawing is a type of graph drawing in which the vertices of a directed graph are drawn in horizontal rows or...

intersection graph of the intervals. Interval graphs are chordal graphs and perfect graphs. They can be recognized in linear time, and an optimal graph coloring...

In graph theory, a graph is said to be a pseudorandom graph if it obeys certain properties that random graphs obey with high probability. There is no concrete...

the mathematical field of graph theory, the Schläfli graph, named after Ludwig Schläfli, is a 16-regular undirected graph with 27 vertices and 216 edges...

NebulaGraph is a free software distributed graph database built for super large-scale graphs with milliseconds of latency. NebulaGraph adopts the Apache...

Named graphs are a key concept of Semantic Web architecture in which a set of Resource Description Framework statements (a graph) are identified using...

Propagation graphs are a mathematical modelling method for radio propagation channels. A propagation graph is a signal flow graph in which vertices represent...

In graph theory, the Laman graphs are a family of sparse graphs describing the minimally rigid systems of rods and joints in the plane. Formally, a Laman...

In graph theory, a locally linear graph is an undirected graph in which every edge belongs to exactly one triangle. Equivalently, for each vertex of the...

makes extensive use of graphs to better illustrate the economic principles and trends it is attempting to explain. Those graphs have specific qualities...

In the mathematical field of graph theory, the Brinkmann graph is a 4-regular graph with 21 vertices and 42 edges discovered by Gunnar Brinkmann in 1992...

Tanner graph is a bipartite graph that can be used to express constraints (typically equations) that specify an error correcting code. Tanner graphs play...

particularly in game theory and mathematical economics, a function is graph continuous if its graph—the set of all input-output pairs—is a closed set in the product...

GraphML is an XML-based file format for graphs. The GraphML file format results from the joint effort of the graph drawing community to define a common...

In graph theory, a moral graph is used to find the equivalent undirected form of a directed acyclic graph. It is a key step of the junction tree algorithm...

The Knowledge Graph is a knowledge base from which Google serves relevant information in an infobox beside its search results. This allows the user to...

traditional Markdown links. Links appear in Obsidian's interactive graph view. The graph view is a visualization of notes in the vault and the connections...

Comparability graphs have also been called transitively orientable graphs, partially orderable graphs, containment graphs, and divisor graphs. An incomparability...

A citation graph (or citation network), in information science and bibliometrics, is a directed graph that describes the citations within a collection...

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...

DOT is a graph description language, developed as a part of the Graphviz project. DOT graphs are typically stored as files with the .gv or .dot filename...

area of graph theory, a triangle-free graph is an undirected graph in which no three vertices form a triangle of edges. Triangle-free graphs may be equivalently...

crystallography, a periodic graph or crystal net is a three-dimensional periodic graph, i.e., a three-dimensional Euclidean graph whose vertices or nodes...

tree is a subset of the edges of a connected, edge-weighted undirected graph that connects all the vertices together, without any cycles and with the...

In the mathematical field of graph theory, the Desargues graph is a distance-transitive, cubic graph with 20 vertices and 30 edges. It is named after...

Sequence graph, also called an alignment graph, breakpoint graph, or adjacency graph, are bidirected graphs used in comparative genomics. The structure...

In graph theory, a k-degenerate graph is an undirected graph in which every subgraph has at least one vertex of degree at most k {\displaystyle k} . That...

In graph theory, a king's graph is a graph that represents all legal moves of the king chess piece on a chessboard where each vertex represents a square...

In geometric graph theory, a branch of mathematics, a matchstick graph is a graph that can be drawn in the plane in such a way that its edges are line...

In the mathematical field of graph theory, the Tutte graph is a 3-regular graph with 46 vertices and 69 edges named after W. T. Tutte. It has chromatic...

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...

In mathematics, a bishop's graph is a graph that represents all legal moves of the chess piece the bishop on a chessboard. Each vertex represents a square...

In graph theory, an outerplanar graph is a graph that has a planar drawing for which all vertices belong to the outer face of the drawing. Outerplanar...

In graph theory, the Cartesian product G □ H of graphs G and H is a graph such that: the vertex set of G □ H is the Cartesian product V(G) × V(H); and...

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 been...

In the mathematical domain of graph theory, a bidirected graph (introduced by Edmonds & Johnson 1970) is a graph in which each edge is given an independent...

field of graph theory, the Clebsch graph is either of two complementary graphs on 16 vertices, a 5-regular graph with 40 edges and a 10-regular graph with...

In mathematics, a convex graph may be a convex bipartite graph a convex plane graph the graph of a convex function This disambiguation page lists articles...

Algebraic graph theory is a branch of mathematics in which algebraic methods are applied to problems about graphs. This is in contrast to geometric, combinatorial...

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...

graph-tool is a Python module for manipulation and statistical analysis of graphs (AKA networks). The core data structures and algorithms of graph-tool...

topological graph theory, a ribbon graph is a way to represent graph embeddings, equivalent in power to signed rotation systems and graph-encoded maps...

GraphQL is a data query and manipulation language that allows specifying what data is to be retrieved ("declarative data fetching") or modified. A GraphQL...

In the mathematical study of graph theory, a pancyclic graph is a directed graph or undirected graph that contains cycles of all possible lengths from...

In graph theory, the generalized Petersen graphs are a family of cubic graphs formed by connecting the vertices of a regular polygon to the corresponding...

An ordered graph is a graph with a total order over its nodes. In an ordered graph, the parents of a node are the nodes that are adjacent to it and precede...

A flow graph is a form of digraph associated with a set of linear algebraic or differential equations: "A signal flow graph is a network of nodes (or points)...

vertex coloring game on a graph G with k colors. Does she have one for k+1 colors? More unsolved problems in mathematics The graph coloring game is a mathematical...

In graph theory, a branch of mathematics, graph canonization is the problem of finding a canonical form of a given graph G. A canonical form is a labeled...

a power graph from a graph (networks). Power graph analysis can be thought of as a lossless compression algorithm for graphs. It extends graph syntax with...

In mathematics, particularly geometric graph theory, a unit distance graph is a graph formed from a collection of points in the Euclidean plane by connecting...

the superposition of a graph (the link graph) and a set of trees (the place graph). Each node of the bigraph is part of a graph and also part of some tree...

In graph theory, a forcing graph is one whose density determines whether a graph sequence is quasi-random. The term was first coined by Chung, Graham...

whose interiors are disjoint. The intersection graph of a circle packing, called a coin graph, is the graph having a vertex for each circle, and an edge...

Graph expansion may refer to: Expander graph Homeomorphism (graph theory) This disambiguation page lists articles associated with the title Graph expansion...

graph theory, a string graph is an intersection graph of curves in the plane; each curve is called a "string". Given a graph G, G is a string graph if...

In graph theory, a biconnected graph is a connected and "nonseparable" graph, meaning that if any one vertex were to be removed, the graph will remain...

In graph theory, a branch of mathematics, an undirected graph is called an asymmetric graph if it has no nontrivial symmetries. Formally, an automorphism...

In graph theory, toughness is a measure of the connectivity of a graph. A graph G is said to be t-tough for a given real number t if, for every integer...

mathematical field of graph theory, a prism graph is a graph that has one of the prisms as its skeleton. The individual graphs may be named after the...

Force-directed graph drawing algorithms are a class of algorithms for drawing graphs in an aesthetically-pleasing way. Their purpose is to position the...

A gain graph is a graph whose edges are labelled "invertibly", or "orientably", by elements of a group G. This means that, if an edge e in one direction...

25). Exponential growth curves are often depicted on a logarithmic scale graph. The markings on slide rules are arranged in a log scale for multiplying...

In the mathematical field of graph theory, a graph G is symmetric or arc-transitive if, given any two ordered pairs of adjacent vertices ( u 1 , v 1 )...

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...

the mathematical field of graph theory, a toroidal graph is a graph that can be embedded on a torus. In other words, the graph's vertices and edges can be...

mathematical field of graph theory, the Foster graph is a bipartite 3-regular graph with 90 vertices and 135 edges. The Foster graph is Hamiltonian and has...

A Reeb graph (named after Georges Reeb by René Thom) is a mathematical object reflecting the evolution of the level sets of a real-valued function on...

JanusGraph is an open source, distributed graph database under The Linux Foundation. JanusGraph is available under the Apache License 2.0. The project...

In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights...

and topology, closed graph is a property of functions. A real function y = f ( x ) {\displaystyle y=f(x)} is closed if the graph is closed, meaning that...

mathematics, the concept of graph dynamical systems can be used to capture a wide range of processes taking place on graphs or networks. A major theme...

In the mathematical field of graph theory, a distance-regular graph is a regular graph such that for any two vertices v and w, the number of vertices...

In the mathematical theory of directed graphs, a graph is said to be strongly connected if every vertex is reachable from every other vertex. The strongly...

a universal graph is an infinite graph that contains every finite (or at-most-countable) graph as an induced subgraph. A universal graph of this type...

the Perkel graph, named after Manley Perkel, is a 6-regular graph with 57 vertices and 171 edges. It is the unique distance-regular graph with intersection...

mathematical field of graph theory, the McGee graph or the (3-7)-cage is a 3-regular graph with 24 vertices and 36 edges. The McGee graph is the unique (3...

area of graph theory, a directed graph is said to be aperiodic if there is no integer k > 1 that divides the length of every cycle of the graph. Equivalently...

In essence, extremal graph theory studies how global properties of a graph influence local substructure. Results in extremal graph theory deal with quantitative...

In the mathematical field of graph theory, the Möbius–Kantor graph is a symmetric bipartite cubic graph with 16 vertices and 24 edges named after August...

Cyclomatic complexity is computed using the control-flow graph of the program. The nodes of the graph correspond to indivisible groups of commands of a program...

In graph theory, a part of mathematics, a k-partite graph is a graph whose vertices are (or can be) partitioned into k different independent sets. Equivalently...

In graph theory, Grassmann graphs are a special class of simple graphs defined from systems of subspaces. The vertices of the Grassmann graph Jq(n, k)...

In graph theory, the diameter of a connected undirected graph is the farthest distance between any two of its vertices. That is, it is the diameter of...

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...

InfiniteGraph is a distributed graph database implemented in Java and C++ and is from a class of NOSQL ("Not Only SQL") database technologies that focus...

In mathematical logic and graph theory, an implication graph is a skew-symmetric, directed graph G = (V, E) composed of vertex set V and directed edge...

In the mathematical field of graph theory, the Ljubljana graph is an undirected bipartite graph with 112 vertices and 168 edges, rediscovered in 2002 and...

global graph intelligence company that provides technology for analyzing and managing connected data. It is most known for creating the Neo4j Graph database...

In graph theory, the girth of an undirected graph is the length of a shortest cycle contained in the graph. If the graph does not contain any cycles (that...

In graph theory, a Halin graph is a type of planar graph, constructed by connecting the leaves of a tree into a cycle. The tree must have at least four...

In graph theory, a random geometric graph (RGG) is the mathematically simplest spatial network, namely an undirected graph constructed by randomly placing...

The Turán graph, denoted by T ( n , r ) {\displaystyle T(n,r)} , is a complete multipartite graph; it is formed by partitioning a set of n {\displaystyle...

In graph theory, a branch of mathematics, many important families of graphs can be described by a finite set of individual graphs that do not belong to...

they are not abstract in the sense of the objects in graph 1 below. We might look at other graphs, in a progression from cat to mammal to animal, and see...

the mathematical field of graph theory, the Erdős–Rényi models are two closely related models for generating random graphs and the evolution of a random...

In graph theory, an orientation of an undirected graph is an assignment of a direction to each edge, turning the initial graph into a directed graph. A...

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, …...

In the mathematical field of graph theory, a path graph (or linear graph) is a graph whose vertices can be listed in the order v1, v2, ..., vn such that...

In graph theory, a loop (also called a self-loop or a buckle) is an edge that connects a vertex to itself. A simple graph contains no loops. Depending...

In graph theory, an independent set, stable set, coclique or anticlique is a set of vertices in a graph, no two of which are adjacent. That is, it is a...

In graph theory, two graphs G {\displaystyle G} and G ′ {\displaystyle G'} are homeomorphic if there is a graph isomorphism from some subdivision of G...

In computer science, an e-graph is a data structure that stores an equivalence relation over terms of some language. Let Σ {\displaystyle \Sigma } be...

In graph theory, a branch of mathematics, the disjoint union of graphs is an operation that combines two or more graphs to form a larger graph. It is...

In the mathematical field of graph theory, the 26-fullerene graph is a polyhedral graph with V = 26 vertices and E = 39 edges. Its planar embedding has...

Henson graphs have the finite model property? More unsolved problems in mathematics In graph theory, the Henson graph Gi is an undirected infinite graph, the...

A flame graph is a software profiling visualization technique that allows for the rapid identification of hot spots in computer programs from stack trace...

In graph theory, a branch of mathematics, a map graph is an undirected graph formed as the intersection graph of finitely many simply connected and internally...

The Open Graph Protocol is a specialized web page protocol used between client devices (computers, mobile phones, tablets, etc.). The protocol was initially...

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...

A conceptual graph (CG) is a formalism for knowledge representation. In the first published paper on CGs, John F. Sowa used them to represent the conceptual...

graph theory, a polygon-circle graph is an intersection graph of a set of convex polygons all of whose vertices lie on a common circle. These graphs have...

In graph theory, a cop-win graph is an undirected graph on which the pursuer (cop) can always win a pursuit–evasion game against a robber, with the players...

representation of a simple graph is a method of representing a graph using vector spaces and the dot product from linear algebra. Every graph has a dot product...

In graph theory, the graph removal lemma states that when a graph contains few copies of a given subgraph, then all of the copies can be eliminated by...

right. One of the oldest and most accessible parts of combinatorics is graph theory, which by itself has numerous natural connections to other areas...

In the study of graph algorithms, an implicit graph representation (or more simply implicit graph) is a graph whose vertices or edges are not represented...

In graph theory, a bivariegated graph is a graph whose vertex set can be partitioned into two equal parts such that each vertex is adjacent to exactly...

In graph theory, the Shannon capacity of a graph is a graph invariant defined from the number of independent sets of strong graph products. It is named...

In the mathematical field of graph theory, the Goldner–Harary graph is a simple undirected graph with 11 vertices and 27 edges. It is named after Anita...

In graph theory, the Krackhardt kite graph is a simple graph with ten nodes. The graph is named after David Krackhardt, a researcher of social network...

In graph theory, a book graph (often written B p {\displaystyle B_{p}}  ) may be any of several kinds of graph formed by multiple cycles sharing an edge...

In graph theory, a cut is a partition of the vertices of a graph into two disjoint subsets. Any cut determines a cut-set, the set of edges that have one...

simplex graph of a complete graph is a hypercube graph, and the simplex graph of a cycle graph of length four or more is a gear graph. The simplex graph of...

A wait-for graph in computer science is a directed graph used for deadlock detection in operating systems and relational database systems. In computer...

A trellis is a graph whose nodes are ordered into vertical slices (time) with every node at almost every time connected to at least one node at an earlier...

In the mathematical area of graph theory, a contact graph or tangency graph is a graph whose vertices are represented by geometric objects (e.g. curves...

Microsoft Graph is a Microsoft API developer platform that connects multiple services and devices. Initially released in November 2015 as Office 365 Unified...

Graph Modeling Language (GML) is a hierarchical ASCII-based file format for describing graphs. It has been also named Graph Meta Language. A simple graph...

field of graph theory, the Coxeter graph is a 3-regular graph with 28 vertices and 42 edges. It is one of the 13 known cubic distance-regular graphs. It is...

mathematical field of graph theory, a graph G is said to be hypohamiltonian if G itself does not have a Hamiltonian cycle but every graph formed by removing...

{\displaystyle k\in \mathbb {N} } , a k {\displaystyle k} -graph (also known as a higher-rank graph or graph of rank k {\displaystyle k} ) is a countable category...

topology and graph theory, a map is a subdivision of a surface such as the Euclidean plane into interior-disjoint regions, formed by embedding a graph onto the...

In the mathematical field of graph theory, a word-representable graph is a graph that can be characterized by a word (or sequence) whose entries alternate...

In graph theory, the graph bandwidth problem may be visualized as placing the vertices of a given graph at distinct integer positions along the number...

In mathematics and computational geometry, the Gabriel graph of a set S {\displaystyle S} of points in the Euclidean plane expresses one notion of proximity...

In computational geometry, the Urquhart graph of a set of points in the plane, named after Roderick B. Urquhart, is obtained by removing the longest edge...

graph theory, the Robertson–Seymour theorem (also called the graph minors theorem) states that the undirected graphs, partially ordered by the graph minor...

In the mathematical field of graph theory, a permutation graph is a graph whose vertices represent the elements of a permutation, and whose edges represent...

Turi is a graph-based, high performance, distributed computation framework written in C++. The GraphLab project was started by Prof. Carlos Guestrin of...

Deficiency is a concept in graph theory that is used to refine various theorems related to perfect matching in graphs, such as Hall's marriage theorem...

GSS (Graph Style Sheets) in mathematics and computing, is an RDF (Resource Description Framework) vocabulary for representation of data in a model of...

design and analysis of algorithms, with work in combinatorial optimization, graph partitioning, network flow, metric embeddings, and computational biology...

In the mathematical field of graph theory, the Horton graph or Horton 96-graph is a 3-regular graph with 96 vertices and 144 edges discovered by Joseph...

In representation learning, knowledge graph embedding (KGE), also called knowledge representation learning (KRL), or multi-relation learning, is a machine...

A hockey stick graph or hockey stick curve is a graph, or curve shape, that resembles an ice hockey stick, in that it turns sharply from a nearly flat...

an algorithm for finding the shortest paths between nodes in a weighted graph, which may represent, for example, a road network. It was conceived by computer...

self-complementary graph, a block graph, a split graph, an interval graph, a claw-free graph, a 1-vertex-connected graph and a 1-edge-connected graph. A graph is bull-free...

In graph theory, a well-covered graph is an undirected graph in which the minimal vertex covers all have the same size. Here, a vertex cover is a set...

In graph theory, the thickness of a graph G is the minimum number of planar graphs into which the edges of G can be partitioned. That is, if there exists...

In graph theory and computer science, the graph sandwich problem is a problem of finding a graph that belongs to a particular family of graphs and is...

the mathematics of infinite graphs, an end of an undirected graph represents, intuitively, a direction in which the graph extends to infinity. Ends may...

Unsolved problem in mathematics Does there exist a conference graph for every number of vertices v > 1 {\displaystyle v>1} where v ≡ 1 mod 4 {\displaystyle...

mathematics, calculus on finite weighted graphs is a discrete calculus for functions whose domain is the vertex set of a graph with a finite number of vertices...

The nullity of a graph in the mathematical subject of graph theory can mean either of two unrelated numbers. If the graph has n vertices and m edges, then:...

-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 d'}...

In graph theory, an area of mathematics, a claw-free graph is a graph that does not have a claw as an induced subgraph. A claw is another name for the...

In graph theory, a tournament is a directed graph with exactly one edge between each two vertices, in one of the two possible directions. Equivalently...

mathematical field of graph theory, a quartic graph is a graph where all vertices have degree 4. In other words, a quartic graph is a 4-regular graph. Several well-known...

In graph theory and recreational mathematics, the Hanoi graphs are undirected graphs whose vertices represent the possible states of the Tower of Hanoi...

regular graphs are vertex-transitive (for example, the Frucht graph and Tietze's graph). Finite vertex-transitive graphs include the symmetric graphs (such...

graph theory, an adjacent vertex of a vertex v in a graph is a vertex that is connected to v by an edge. The neighbourhood of a vertex v in a graph G...

In graph theory, a split of an undirected graph is a cut whose cut-set forms a complete bipartite graph. A graph is prime if it has no splits. The splits...

Node graph architecture is a software design structured around the notion of a node graph. Both the source code and the user interface are designed around...

In graph theory, a vertex is incident with an edge if the vertex is one of the two vertices the edge connects. An incidence is a pair ( u , e ) {\displaystyle...

In graph theory, the Weisfeiler Leman graph isomorphism test is a heuristic test for the existence of an isomorphism between two graphs G and H. It is...

plot is a graphical technique for representing a data set, usually as a graph showing the relationship between two or more variables. The plot can be...

hypergraph is a generalization of a graph in which an edge can join any number of vertices. In contrast, in an ordinary graph, an edge connects exactly two...

of graph theory, a self-complementary graph is a graph which is isomorphic to its complement. The simplest non-trivial self-complementary graphs are...

graph theory, the crossing number cr(G) of a graph G is the lowest number of edge crossings of a plane drawing of the graph G. For instance, a graph is...

In natural language processing (NLP), a text graph is a graph representation of a text item (document, passage or sentence). It is typically created as...

Graphism is the expression of thought in material symbols. Graphism began some 30,000 years BC, not as a photographic representation of reality but as...

r-regular graph is a graph selected from G n , r {\displaystyle {\mathcal {G}}_{n,r}} , which denotes the probability space of all r-regular graphs on n {\displaystyle...

In mathematics, a flip graph is a graph whose vertices are combinatorial or geometric objects, and whose edges link two of these objects when they can...

In graph theory, the strong product is a way of combining two graphs to make a larger graph. Two vertices are adjacent in the strong product when they...

In graph theory, a branch of mathematics, a skew-symmetric graph is a directed graph that is isomorphic to its own transpose graph, the graph formed by...

A line chart or line graph, also known as curve chart, is a type of chart that displays information as a series of data points called 'markers' connected...

In graph theory, a geodetic graph is an undirected graph such that there exists a unique (unweighted) shortest path between each two vertices. Geodetic...

In graph theory, the star Sk is the complete bipartite graph K1, k, that is, it is a tree with one internal node and k leaves. Alternatively, some authors...

In graph theory, a Meyniel graph is a graph in which every odd cycle of length five or more has at least two chords (edges connecting non-consecutive vertices...

of graph theory, the Hoffman–Singleton graph is a 7-regular undirected graph with 50 vertices and 175 edges. It is the unique strongly regular graph with...

graphs SCG ( k ) {\displaystyle {\text{SCG}}(k)} . In mathematics, especially graph theory, a simple subcubic graph (SSCG) is a finite simple graph in...

discipline of graph theory, the (m,n)-tadpole graph is a special type of graph consisting of a cycle graph on m (at least 3) vertices and a path graph on n vertices...

In the mathematical field of graph theory, the Meringer graph is a 5-regular undirected graph with 30 vertices and 75 edges named after Markus Meringer...

In Unix, graph is a command-line utility used to draw plots from tabular data. The graph utility, written by Douglas McIlroy, was present in the first...

Circulant graph, a graph with cyclic symmetry Cycle (graph theory), a nontrivial path in some graph from a node to itself Cyclic graph, a graph containing...

technology studies (STS), the graphism thesis is a proposition advanced by Bruno Latour that visual inscriptions—especially graphs, diagrams, and other visual...

mathematical and algorithmic study of graph theory, the converse, transpose or reverse of a directed graph G is another directed graph on the same set of vertices...

In graph theory, Vizing's theorem states that every simple undirected graph may be edge colored using a number of colors that is at most one larger than...

In graph theory, an Andrásfai graph is a triangle-free, circulant graph named after Béla Andrásfai. The Andrásfai graph And(n) for any natural number n...

A Graph Coarsening Algorithm is a family of metaheuristic algorithms used to reduce the size and complexity of a large graph while preserving its key structural...

Facebook Graph Search was a semantic search engine that Facebook introduced in March 2013. It was designed to give answers to user natural language queries...

cycle graph of a group is an undirected graph that illustrates the various cycles of that group, given a set of generators for the group. Cycle graphs are...

of graph theory, a cage is a regular graph that has as few vertices as possible for its girth. Formally, an (r, g)-graph is defined to be a graph in which...

dependence graphs (PDG) at statement and predicate nodes. The resulting graph is a property graph, which is the underlying graph model of graph databases...

In graph theory, Kuratowski's theorem is a mathematical forbidden graph characterization of planar graphs, named after Kazimierz Kuratowski. It states...

The graph of desire (French: graphe du désir) is a conceptual tool in Lacanianism. Lacan devised numerous quasi-mathematical diagrams to represent the...

In mathematics, the McKay graph of a finite-dimensional representation V of a finite group G is a weighted quiver encoding the structure of the representation...

A chart (sometimes known as a graph) is a graphical representation for data and information visualization, in which "the data is represented by symbols...

The center (or Jordan center) of a graph is the set of all vertices of minimum eccentricity, that is, the set of all vertices u where the greatest distance...

graph theory, the medial graph of plane graph G is another graph M(G) that represents the adjacencies between edges in the faces of G. Medial graphs were...

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...

Cypher is a declarative graph query language that allows for expressive and efficient data querying in a property graph. Cypher was largely an invention...

In graph theory, a cactus (sometimes called a cactus tree) is a connected graph in which any two simple cycles have at most one vertex in common. Equivalently...

In graph theory, the planarity testing problem is the algorithmic problem of testing whether a given graph is a planar graph (that is, whether it can...

In graph theory and statistics, a graphon (also known as a graph limit) is a symmetric measurable function W : [ 0 , 1 ] 2 → [ 0 , 1 ] {\displaystyle...

In graph theory, an arborescence is a directed graph where there exists a vertex r (called the root) such that, for any other vertex v, there is exactly...

In graph theory, the Frucht graph is a cubic graph with 12 vertices, 18 edges, and no nontrivial symmetries. It was first described by Robert Frucht in...

graph traversal language and virtual machine developed by Apache TinkerPop of the Apache Software Foundation. Gremlin works for both OLTP-based graph...

mathematical field of graph theory, a core is a notion that describes behavior of a graph with respect to graph homomorphisms. Graph C {\displaystyle C}...

The k-semi-Yao graph (k-SYG) of a set of n objects P is a geometric proximity graph, which was first described to present a kinetic data structure for...

computer science, a topological sort or topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge (u...

In the mathematics of graph theory and finite groups, a prime graph is an undirected graph defined from a group. These graphs were introduced in a 1981...

can be formalized as a problem in topological graph theory by asking whether the complete bipartite graph K 3 , 3 {\displaystyle K_{3,3}} , with vertices...

graph theory, a branch of mathematics, the rank of an undirected graph has two unrelated definitions. Let n equal the number of vertices of the graph...

In statistics and Markov modeling, an ancestral graph is a type of mixed graph used to provide a graphical representation for the result of marginalizing...

HMS Graph (pennant number P715) was a German Type VIIC U-boat captured and recommissioned by the British Royal Navy during World War II. Commissioned...

mathematical field of graph theory, the distance between two vertices in a graph is the number of edges in a shortest path (also called a graph geodesic) connecting...

In complex analysis, domain coloring or a color wheel graph is a technique for visualizing complex functions by assigning a color to each point of the...

In graph theory, a branch of mathematics, an apex graph is a graph that can be made planar by the removal of a single vertex. The deleted vertex is called...

graph theory, a semi-symmetric graph is an undirected graph that is edge-transitive and regular, but not vertex-transitive. In other words, a graph is...

Pan-genome graph construction is the process of creating a graph-based representation of the collective genome (the pan-genome) of a species or a group...

An existential graph is a type of diagrammatic or visual notation for logical expressions, created by Charles Sanders Peirce, who wrote on graphical logic...

Hockey stick graphs present global or hemispherical mean global surface temperatures of the distant past, as shown by quantitative climate reconstructions...

NetworkX is a Python library for studying graphs and networks. NetworkX is free software released under the BSD-new license. NetworkX began development...

the given graph. Perfectly orderable graphs form a special case of the perfect graphs, and they include the chordal graphs, comparability graphs, and distance-hereditary...

computer science, graph edit distance (GED) is a measure of similarity (or dissimilarity) between two graphs. The concept of graph edit distance was first...

mathematical graph theory, the Higman–Sims graph is a 22-regular undirected graph with 100 vertices and 1100 edges. It is the unique strongly regular graph srg(100...

In graph theory, a critical graph is an undirected graph all of whose proper subgraphs have smaller chromatic number. In such a graph, every vertex or...

In mathematics, a graph C*-algebra is a universal C*-algebra constructed from a directed graph. Graph C*-algebras are direct generalizations of the Cuntz...

form of a directed acyclic graph with a single source vertex (a vertex with no incoming edges), in which each edge of the graph is labeled by a letter or...

In graph theory, the strong perfect graph theorem is a forbidden graph characterization of the perfect graphs as being exactly the graphs that have neither...

In graph theory, the outer boundary of a subset S of the vertices of a graph G is the set of vertices in G that are adjacent to vertices in S, but not...

In graph theory, a threshold graph is a graph that can be constructed from a one-vertex graph by repeated applications of the following two operations:...

In topology, a graph manifold (in German: Graphenmannigfaltigkeit) is a 3-manifold which is obtained by gluing some circle bundles. They were discovered...

frequent retraining. GraphRAG (coined by Microsoft Research) is a technique that extends RAG with the use of a knowledge graph to allow the model to...

In graph theory, a branch of mathematics, the modular graphs are undirected graphs in which every three vertices x, y, and z have at least one median...

In graph theory, the shift graph Gn,k for n , k ∈ N ,   n > 2 k > 0 {\displaystyle n,k\in \mathbb {N} ,\ n>2k>0} is the graph whose vertices correspond...

In graph theory, a cograph, or complement-reducible graph, or P4-free graph, is a graph that can be generated from the single-vertex graph K1 by complementation...

The nearest neighbor graph (NNG) is a directed graph defined for a set of points in a metric space, such as the Euclidean distance in the plane. The NNG...

In the mathematical field of graph theory, the Meredith graph is a 4-regular undirected graph with 70 vertices and 140 edges discovered by Guy H. J. Meredith...

In graph theory, the tensor product G × H of graphs G and H is a graph such that the vertex set of G × H is the Cartesian product V(G) × V(H); and vertices...

In the mathematical field of graph theory, a distance-transitive graph is a graph such that, given any two vertices v and w at any distance i, and any...

In graph theory, the perfect graph theorem of László Lovász (1972a, 1972b) states that an undirected graph is perfect if and only if its complement graph...

In graph theory, a BF-graph is a type of directed hypergraph where each hyperedge is directed either to one particular vertex or away from one particular...

Trivial Graph Format (TGF) is a simple text-based adjacency list file format for describing graphs, widely used because of its simplicity. The format consists...

In graph theory, a connected graph G is said to be k-vertex-connected (or k-connected) if it has more than k vertices and remains connected whenever fewer...

In graph theory, a trivially perfect graph is a graph with the property that in each of its induced subgraphs the size of the maximum independent set equals...

known as Fiedler value or Fiedler eigenvalue after Miroslav Fiedler) of a graph G is the second-smallest eigenvalue (counting multiple eigenvalues separately)...

In graph theory, the Berlekamp–Van Lint–Seidel graph is a locally linear strongly regular graph with parameters ( 243 , 22 , 1 , 2 ) {\displaystyle (243...

In science and engineering, a semi-log plot/graph or semi-logarithmic plot/graph has one axis on a logarithmic scale, the other on a linear scale. It is...

In the mathematical area of graph theory, a chordal bipartite graph is a bipartite graph B = (X,Y,E) in which every cycle of length at least 6 in B has...

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...

WHO reports, tables, and spreadsheets. There are also maps and timeline graphs of daily and weekly deaths worldwide. 7,114,238 (updated 28 May 2026) confirmed...

geometric graph theory, a unit disk graph is the intersection graph of a family of unit disks in the Euclidean plane. That is, it is a graph with one vertex...

In graph theory, a maximal independent set (MIS) or maximal stable set is an independent set that is not a subset of any other independent set. In other...

specifically in combinatorial commutative algebra, a zero-divisor graph is an undirected graph representing the zero divisors of a commutative ring. It has...

term Steiner tree problem, is the Steiner tree problem in graphs. Given an undirected graph with non-negative edge weights and a subset of vertices, usually...

of graph theory, the sphericity of a graph is a graph invariant defined to be the smallest dimension of Euclidean space required to realize the graph as...

Spatial and Graph, formerly Oracle Spatial, is a free option component of the Oracle Database. The spatial features in Oracle Spatial and Graph aid users...

In graph theory, a clique graph of an undirected graph G is another graph K(G) that represents the structure of cliques in G. Clique graphs were discussed...

In graph theory, the treewidth of an undirected graph is an integer number which specifies, informally, how far the graph is from being a tree. The smallest...

In graph theory, a Harris graph is defined as an Eulerian, tough, non-Hamiltonian graph. Harris graphs were introduced in 2013 when, at the University...

are used to determine whether some combinatorial structure S (such as a graph or a boolean function) satisfies some property P, or is "far" from having...

In the mathematical field of graph theory, the Walther graph, also called the Tutte fragment, is a planar bipartite graph with 25 vertices and 31 edges...

octahedron give rise to a graph, a discrete structure drawn in a plane. The name is octahedral graph. The octahedral graph is an example of a four-connected...

mathematics, a bouquet graph B m {\displaystyle B_{m}} , for an integer parameter m {\displaystyle m} , is an undirected graph with one vertex and m {\displaystyle...

well-connected. Consider, for example, the following graph: Three communities are present in this graph (each color represents a community). Additionally...

tree or graph data structures. The algorithm starts at the root node (selecting some arbitrary node as the root node in the case of a graph) and explores...

Unsolved problem in mathematics Conjecture: A graph G with Δ ( G ) > n / 3 {\displaystyle \Delta (G)>n/3} is class 2 if and only if it has an overfull...

GTK Scene Graph Kit (GSK) is the rendering and scene graph API for GTK introduced with version 3.90. GSK lies between the graphical control elements (widgets)...

In graph theory, the modular product of graphs G and H is a graph formed by combining G and H that has applications to subgraph isomorphism. It is one...

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...

In graph theory, a class of graphs is said to have few cliques if every member of the class has a polynomial number of maximal cliques. Certain generally...

In graph theory, the Grundy number or Grundy chromatic number of an undirected graph is the maximum number of colors that can be used by a greedy coloring...

datasets. HNSW stores vectors in a graph. Each vector is a node, and links connect it to some nearby vectors. The graph has several layers: upper layers...

In graph theory, a bound graph expresses which pairs of elements of some partially ordered set have an upper bound. Rigorously, any graph G is a bound...

In extremal graph theory, given a graph H {\displaystyle H} , a graph G {\displaystyle G} is said to be H {\displaystyle H} -saturated if G {\displaystyle...

In the mathematical field of graph theory, a transitive reduction of a directed graph D is another directed graph with the same vertices and as few edges...

In graph theory, a haven is a certain type of function on sets of vertices in an undirected graph. If a haven exists, it can be used by an evader to win...

An Erdős–Diophantine graph is an object in the mathematical subject of Diophantine equations consisting of a set of integer points at integer distances...

In computational geometry, the relative neighborhood graph (RNG) is an undirected graph defined on a set of points in the Euclidean plane by connecting...

In mathematics, a k-ultrahomogeneous graph is a graph in which every isomorphism between two of its induced subgraphs of at most k vertices can be extended...

A chemical graph generator is a software package to generate computer representations of chemical structures adhering to certain boundary conditions....

Malak, Michael (14 June 2016). "Finding Graph Isomorphisms In GraphX And GraphFrames: Graph Processing vs. Graph Database". slideshare.net. sparksummit...