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Mathematical model used by graph-oriented databases
A property graph, labeled property graph, or attributed graph is a data model of various graph-oriented databases, where pairs of entities are associated
Property_graph
Query language for property graphs
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
Graph_Query_Language
Representation of a computer program
property graph (CPG) is a computer program representation that captures syntactic structure, control flow, and data dependencies in a property graph.
Code_property_graph
Property of graphs that depends only on abstract structure
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
Graph_property
Database using graph structures for queries
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
Graph_database
2023 edition of the SQL standard
grouped into three main areas: Property graph queries, a graph query language built on top of SQL The new part 16, “Property Graph Queries (SQL/PGQ)”, has been
SQL:2023
Declarative graph query language
Cypher is a declarative graph query language that allows for expressive and efficient data querying in a property graph. Cypher was largely an invention
Cypher_(query_language)
Area of discrete mathematics
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
Graph_theory
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
Glossary_of_graph_theory
Graph representing edges of another graph
connected graph G can be recovered completely from its line graph. Many other properties of line graphs follow by translating the properties of the underlying
Line_graph
Graph of numbers differing by a square
quadratic residues, and have interesting properties that make them useful in graph theory more generally. Paley graphs are named after Raymond Paley. They
Paley_graph
Matrix representation of a graph
functional graph properties. Kirchhoff's theorem can be used to calculate the number of spanning trees for a given graph. The sparsest cut of a graph can be approximated
Laplacian_matrix
On bipartite matching and vertex cover
In the mathematical area of graph theory, Kőnig's theorem, proved by Dénes Kőnig (1931), describes an equivalence between the maximum matching problem
Kőnig's theorem (graph theory)
Kőnig's_theorem_(graph_theory)
Property of functions in topology
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
Closed_graph_property
Graph generated by a random process
particular property of the graph is likely to arise. Different random graph models produce different probability distributions on graphs. Most commonly
Random_graph
Graph of triangles with a shared vertex
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
Friendship_graph
Topics referred to by the same term
vertices and edges Graph theory, the study of such graphs and their properties Graph (topology), a topological space resembling a graph in the sense of discrete
Graph
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 been
Two-graph
Operation that combines two graphs
In graph theory, the join operation is a graph operation that combines two graphs by connecting every vertex of one graph to every vertex of the other
Join_(graph_theory)
4-regular undirected graph in mathematics
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
Robertson_graph
Infinite graph containing all countable graphs
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
Rado_graph
Graph that can be embedded in the plane
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
Planar_graph
Sparse graph with strong connectivity
In graph theory, an expander graph is a sparse graph that has strong connectivity properties, quantified using vertex, edge or spectral expansion. Expander
Expander_graph
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
Class of artificial neural networks
Graph neural networks (GNNs) are artificial neural networks designed for tasks whose inputs are graphs. Because graphs usually do not have a canonical
Graph_neural_network
Graph representing faces of another graph
embedding of the graph G, so it is a property of plane graphs (graphs that are already embedded in the plane) rather than planar graphs (graphs that may be
Dual_graph
Subgraph with contracted edges
every graph property preserved by deletions and contractions may be recognized in polynomial time. Other results and conjectures involving graph minors
Graph_minor
Undirected graph acted on by a vertex-transitive cyclic group of symmetries
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
Circulant_graph
Graph of chess rook moves
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
Rook's_graph
Graph with nodes connected in a closed chain
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
Cycle_graph
Graph database implemented in Java
development of the Graph Query Language (GQL), an ISO-standardized query language for property graphs, and is a founding member of the GraphQL Foundation,
Neo4j
Directed graph with no directed cycles
In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it
Directed_acyclic_graph
Two closely related models for generating random graphs
existence of graphs satisfying various properties, or to provide a rigorous definition of what it means for a property to hold for almost all graphs. There
Erdős–Rényi_model
Graph defined from a mathematical group
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
Cayley_graph
Cubic graph with 10 vertices and 15 edges
bridgeless graph has a cycle-continuous mapping to the Petersen graph. More unsolved problems in mathematics In the mathematical field of graph theory, the
Petersen_graph
Linear algebra aspects of graph theory
In mathematics, spectral graph theory is the study of the properties of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors
Spectral_graph_theory
Type of knowledge base
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
Knowledge_graph
Topic in computer science
the problem. Typically, property testing algorithms are used to determine whether some combinatorial structure S (such as a graph or a boolean function)
Property_testing
Concept in graph theory
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
Strongly_regular_graph
Graph database product by Amazon
announced on November 29, 2017. Amazon Neptune supports popular graph models property graph and W3C's RDF, and their respective query languages Apache TinkerPop's
Amazon_Neptune
Logical formulation of graph properties
mathematical fields of graph theory and finite model theory, the logic of graphs deals with formal specifications of graph properties using sentences of mathematical
Logic_of_graphs
Information as entities that have properties and relationships to other entities. It is derived from property graphs, with semantics formally defined on
NGSI-LD
Influence of local substructure of a graph on global properties
In essence, extremal graph theory studies how global properties of a graph influence local substructure. Results in extremal graph theory deal with quantitative
Extremal_graph_theory
Concept in game theory
of points on the graph converges, its limit point must also belong to the graph. This concept, related to the closed graph property in functional analysis
Graph_continuous_function
Geospatial and graph component of Oracle Database
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
Oracle_Spatial_and_Graph
Adjacent subset of an undirected graph
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
Clique_(graph_theory)
Derived graph of higher chromatic number
In the mathematical area of graph theory, the Mycielskian or Mycielski graph of an undirected graph is a larger graph formed from it by a construction
Mycielskian
Type of graph
biconnected graph has no articulation vertices. The property of being 2-connected is equivalent to biconnectivity, except that the complete graph of two vertices
Biconnected_graph
Graph database system
a graph database model, which is basically characterized by three properties: data structures are graphs or any other structure similar to a graph; data
Sparksee_(graph_database)
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)
Property of objects inherited by all their subobjects
context. These properties are particularly considered in topology and graph theory, but also in set theory. In topology, a topological property is said to
Hereditary_property
Graph property
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
Distance-regular_graph
Undirected graph with no non-trivial symmetries
nontrivial symmetries. Formally, an automorphism of a graph is a permutation p of its vertices with the property that any two vertices u and v are adjacent if
Asymmetric_graph
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
Graph_C*-algebra
field of graph theory, the Brouwer–Haemers graph is a 20-regular undirected graph with 81 vertices and 810 edges. It is a strongly regular graph, a distance-transitive
Brouwer–Haemers_graph
Planar bipartite graph with 25 vertices and 31 edges
the resulting graph has no Hamiltonian path. This property was used by Tutte when combining three Walther graphs to produce the Tutte graph, the first known
Walther_graph
Geometric graph with unit edge lengths
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
Unit_distance_graph
Spectral graph theory concept
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
Ramanujan_graph
Partition of a graph whose components are reachable from all vertices
connected component of a directed graph G is a subgraph that is strongly connected, and is maximal with this property: no set of additional edges or vertices
Strongly_connected_component
theory. Krackhardt introduced the graph in 1990 to distinguish different concepts of centrality. It has the property that the vertex with maximum degree
Krackhardt_kite_graph
Data storage paradigm in computing
NewSQL databases are supported by ordered key–value stores. JanusGraph, a property graph database, has both a Berkeley DB backend and FoundationDB backend
Ordered_key–value_store
Directed graph representing dependencies
mathematics, computer science and digital electronics, a dependency graph is a directed graph representing dependencies of several objects towards each other
Dependency_graph
Methodic assignment of colors to elements of a graph
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
Graph_coloring
Representation of a mathematical function
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
Graph_of_a_function
Data query language developed by Facebook
or modified. A GraphQL server can process a client query using data from separate sources and present the results in a unified graph. The language is
GraphQL
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
Vertex adjacent to all others in a graph
In graph theory, a universal vertex is a vertex of an undirected graph that is adjacent to all other vertices of the graph. It may also be called a dominating
Universal_vertex
All even-degree subgraphs of a graph
In graph theory, a branch of mathematics, the (binary) cycle space of an undirected graph is the set of its even-degree spanning subgraphs, or the set
Cycle_space
Least-weight tree connecting graph vertices
graph theory, a minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected, edge-weighted undirected graph that
Minimum_spanning_tree
Graph whose biconnected components are all cliques
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
Block_graph
Theorem in graph theory
also has applications to property testing. Let H {\displaystyle H} be a graph with h {\displaystyle h} vertices. The graph removal lemma states that
Graph_removal_lemma
Refinement of perfect matching theorems
theorem. This was first studied by Øystein Ore. A related property is surplus. Let G = (V, E) be a graph, and let U be an independent set of vertices, that is
Deficiency_(graph_theory)
Bipartite 4-regular graph with 20 nodes and 40 edges
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
Folkman_graph
Graph formed by complementation and disjoint union
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
Cograph
Graph representing intersections between given sets
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
Intersection_graph
Mathematical tree of cycles
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
Cactus_graph
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
List_of_graph_theory_topics
Graph related to another graph by a covering map
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
Covering_graph
Regular graph with girth more than twice its diameter
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
Moore_graph
Graph where every edge is in one triangle
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
Locally_linear_graph
Changes of data format without any loss
graph models, such as from the Resource Description Framework (RDF) to Property Graphs and back, ensuring the original semantics and structure are preserved
Round-trip_format_conversion
Order-zero graph or any edgeless graph
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
Null_graph
Theorems connecting continuity to closure of graphs
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
Closed graph theorem (functional analysis)
Closed_graph_theorem_(functional_analysis)
Graph where every connected induced subgraph has a universal vertex
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
Trivially_perfect_graph
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
Partition of a graph into spanning subgraphs
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
Graph_factorization
Directed path algebra
constructed from a directed graph. Leavitt path algebras generalize Leavitt algebras and may be considered as algebraic analogues of graph C*-algebras. Leavitt
Leavitt_path_algebra
Solid with 12 equal pentagonal faces
regular dodecahedron can be represented as the graph called the dodecahedral graph, a Platonic graph. Its property of the Hamiltonian, a path that visits all
Regular_dodecahedron
Proprietary database management system
within a single engine, including relational, JSON document, XML, spatial, graph, text, and AI vector data, all queryable through SQL. Oracle AI Database
Oracle_Database
Topics referred to by the same term
and keys in Google Cloud Datastore Graph Query Language, an international standard property graph query language GraphQL, open-source data query and manipulation
GQL
On linear-time algorithms for graph logic
study of graph algorithms, Courcelle's theorem is the statement that every graph property definable in the monadic second-order logic of graphs can be decided
Courcelle's_theorem
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
Games_graph
Describing a family of graphs by excluding certain (sub)graphs
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
Forbidden graph characterization
Forbidden_graph_characterization
Cartesian product of complete graphs
Hamming graphs are a special class of graphs named after Richard Hamming and used in several branches of mathematics (graph theory) and computer science
Hamming_graph
Graphs formed by a hypercube's edges and vertices
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
Hypercube_graph
Knowledge base to enhance search results
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
Knowledge_Graph_(Google)
World Wide Web Consortium standard
applies. A property shape describes characteristics of graph nodes that can be reached via a specific path. A path can be a single predicate (property) or a
SHACL
Cycle graph plus universal vertex
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
Wheel_graph
Topics referred to by the same term
Go City Labeled property graphs, a widely used graph data model Local Land and Property Gazetteer (LLPG) National Land and Property Gazetteer (NLPG)
LPG
Topics referred to by the same term
Open graph may refer to: A confused version of the Closed graph property The Open Graph Protocol This disambiguation page lists articles associated with
Open_graph
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