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Subdivision of vertices into disjoint sets
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
Graph_partition
Partition of a graph's nodes into 2 disjoint subsets
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
Cut_(graph_theory)
Decomposition of an integer as a sum of positive integers
In number theory and combinatorics, a partition of a non-negative integer n, also called an integer partition, is a way of writing n as a sum of positive
Integer_partition
or an ordered partition of a set, partition of a graph, partition of an integer, partition of an interval, partition of unity, partition of a matrix; see
List_of_partition_topics
Maximal subgraph whose vertices can reach each other
The components of any graph partition its vertices into disjoint sets, and are the induced subgraphs of those sets. A graph that is itself connected
Component_(graph_theory)
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
Quotient_graph
Graph representing edges of another graph
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
Line_graph
Partition of a graph whose components are reachable from all vertices
directed graph form a partition into subgraphs that are strongly connected themselves. It is possible to test the strong connectivity of a graph, or to
Strongly_connected_component
Partition of vertices of a directed graph
In graph theory, the weak components of a directed graph partition the vertices of the graph into subsets that are totally ordered by reachability. They
Weak_component
Software package for graph partitioning
METIS is a software package for graph partitioning that implements various multilevel algorithms. METIS' multilevel approach has three phases and comes
METIS
Graph able to be partitioned into multiple independent sets
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
Multipartite_graph
Partition of a graph by removing fewest possible edges
In graph theory, a minimum cut or min-cut of a graph is a cut (a partition of the vertices of a graph into two disjoint subsets) that is minimal in some
Minimum_cut
American computer scientist and educator
analysis of algorithms, with work in combinatorial optimization, graph partitioning, network flow, metric embeddings, and computational biology. Rao received
Satish_B._Rao
Graph partition into regular subgraphs
In extremal graph theory, Szemerédi's regularity lemma states that a graph can be partitioned into a bounded number of parts so that the edges between
Szemerédi_regularity_lemma
Abstract data type in computer science
science, a graph is an abstract data type that is meant to implement the undirected graph and directed graph concepts from the field of graph theory within
Graph_(abstract_data_type)
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
new, smaller graph. This process is applied iteratively until the graph is small enough. Then, the original problem (such as partitioning or clustering)
Graph_Coarsening_Algorithm
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 which partitions into a clique and independent set
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
Split_graph
Clustering and community detection algorithm
function aggregateGraph returns a new graph whose vertices are the partition of the old graph, and whose edges are calculated using the old graph. This function
Louvain_method
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
Topics referred to by the same term
topological space Plane partition, in mathematics and especially combinatorics Graph partition, the reduction of a graph to a smaller graph Folding screen, a
Partition
Mathematical ways to group elements of a set
common coarsening of them all; in graph-theoretic terms, it is the partition of the vertices of the complete graph into the connected components of the
Partition_of_a_set
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
Canadian computer scientist (born 1942)
well-known heuristics for two NP-complete optimization problems: graph partitioning and the travelling salesman problem. In a display of authorial equity
Brian_Kernighan
Partitioning a digital image into segments
neighborhood pixels. The graph (image) is then partitioned according to a criterion designed to model "good" clusters. Each partition of the nodes (pixels)
Image_segmentation
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
Node ordering for directed acyclic graphs
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
Topological_sorting
In graph theory, a discipline within mathematics, the frequency partition of a graph (simple graph) is a partition of its vertices grouped by their degree
Frequency partition of a graph
Frequency_partition_of_a_graph
Second-smallest eigenvalue of a graph Laplacian
the Fiedler vector. The Fiedler vector can be used to partition a graph. For the example graph in the introductory section, the Fiedler vector is ( 0
Algebraic_connectivity
Clustering and community detection algorithm
highly used quality metric for assessing how well a set of communities partition a graph. The equation for this metric is defined for an adjacency matrix,
Leiden_algorithm
Partition of a graph into spanning subgraphs
k-regular subgraph, and a k-factorization partitions the edges of the graph into disjoint k-factors. A graph G is said to be k-factorable if it admits
Graph_factorization
problem. Feedback vertex set Feedback arc set Graph coloring Graph homomorphism problem Graph partition into subgraphs of specific types (triangles, isomorphic
List_of_NP-complete_problems
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
Graph divided into two independent sets
bipartite graph whose partition has the parts U {\displaystyle U} and V {\displaystyle V} , with E {\displaystyle E} denoting the edges of the graph. If a
Bipartite_graph
Graph representing faces of another graph
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
Dual_graph
Any planar graph can be subdivided by removing a few vertices
O({\sqrt {n}})} vertices from an n-vertex graph (where the O invokes big O notation) can partition the graph into disjoint subgraphs each of which has
Planar_separator_theorem
Sequence of edges which join a sequence of vertices on a given graph
of vertices in weighted directed graphs. The k-path partition problem is the problem of partitioning a given graph to a smallest collection of vertex-disjoint
Path_(graph_theory)
In graph theory, a skew partition of a graph is a partition of its vertices into two subsets, such that the induced subgraph formed by one of the two subsets
Skew_partition
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
Clustering methods
{\displaystyle B_{+}} and the rest in B − {\displaystyle B_{-}} , thus bi-partitioning the graph and labeling the data points with two labels. This sign-based approach
Spectral_clustering
Partition of a graph's nodes into cliques
In graph theory, a clique cover or partition into cliques of a given undirected graph is a collection of cliques that cover the whole graph. Generally
Clique_cover
Balanced complete multipartite graph
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
Turán_graph
Form of data structure
domains and user scenarios. Graph (data structure) Graph theory Space partitioning Tree (data structure) Directed graph Leler, Wm and Merry, Jim (1996)
Scene_graph
On chains and antichains in partial orders
incomparability graph. Therefore, by the De Bruijn–Erdős theorem, P itself also has a w-colorable incomparability graph, and thus has the desired partition into
Dilworth's_theorem
solution of sparse symmetric systems of linear equations based on graph partitioning. Nested dissection was introduced by George (1973); the name was suggested
Nested_dissection
Generalization of graph theory
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
Hypergraph
Topic in computer science
graph property testing was first introduced by Goldreich, Goldwasser, and Ron. In their seminal paper published in 1998, an abstract graph partition problem
Property_testing
or right-resolving map, equitable partition, color refinement, and Weisfeiler–Leman canonical form. A directed graph G {\displaystyle G} is given by a
Fibrations_of_graphs
Subdivision into few independent sets
arboricity of an undirected graph, the minimum number of forests needed to cover all of its edges. Matroid partitioning may be solved in polynomial time
Matroid_partitioning
Optimization technique
optimization (other graph cutting algorithms may be considered as graph partitioning algorithms). "Binary" problems (such as denoising a binary image)
Graph cuts in computer vision and artificial intelligence
Graph_cuts_in_computer_vision_and_artificial_intelligence
concerned with partitioning an image into multiple regions according to some homogeneity criterion. This article is primarily concerned with graph theoretic
Segmentation-based object categorization
Segmentation-based_object_categorization
Graph with tight clique-coloring relation
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
Perfect_graph
Concept in network science
structure in graph data. The stochastic block model takes the following parameters: The number n {\displaystyle n} of vertices; a partition of the vertex
Stochastic_block_model
every countable graph have an unfriendly partition into two parts? More unsolved problems in mathematics In the mathematics of infinite graphs, an unfriendly
Unfriendly_partition
Bijection between the vertex set of two graphs
an equivalence relation on graphs and as such it partitions the class of all graphs into equivalence classes. A set of graphs isomorphic to each other is
Graph_isomorphism
Assignment of colors to edges of a graph
coloring is the same thing as a partition of the graph into disjoint matchings. If the size of a maximum matching in a given graph is small, then many matchings
Edge_coloring
ordering on the sets in the partition. Partition refinement forms a key component of several efficient algorithms on graphs and finite automata, including
Partition_refinement
linear program. Two graphs are also fractionally isomorphic if they have a common coarsest equitable partition. A partition of a graph is a collection of
Fractional_graph_isomorphism
Complexity class
for problems on graphs: Swap - A partition ( P 2 , P 3 ) {\displaystyle (P_{2},P_{3})} of nodes in a graph is a neighbor of a partition ( P 0 , P 1 ) {\displaystyle
PLS_(complexity)
Aspect of mathematical group theory
understand a simple construction. Take a complete graph with 6 vertices, K6. It has 15 edges, which can be partitioned into perfect matchings in 15 different ways
Automorphisms of the symmetric and alternating groups
Automorphisms_of_the_symmetric_and_alternating_groups
Type of geometric spanner graph
involves partitioning the space around each vertex into a set of cones, which themselves partition the remaining vertices of the graph. Like Yao Graphs, a Θ
Theta_graph
Perfect graphs have neither odd holes nor odd antiholes
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
Strong_perfect_graph_theorem
Partition of the vertices of a graph
In graph theory, the Gallai–Edmonds decomposition is a partition of the vertices of a graph into three subsets which provides information on the structure
Gallai–Edmonds_decomposition
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
Graph where all long cycles have a chord
chordal graph may be found efficiently using an algorithm known as lexicographic breadth-first search. This algorithm maintains a partition of the vertices
Chordal_graph
Mathematical propositions in network flow theory
have enabled the development of approximation algorithms for use in graph partition and related problems, where finding the absolute best solution is computationally
Approximate max-flow min-cut theorem
Approximate_max-flow_min-cut_theorem
In graph theory, a branch of mathematics, an equitable partition of the vertex set V of a graph G = (V, E) is a partition of V such that, for any pair
Equitable_partition
In graph theory, the Graham–Pollak theorem states that the edges of an n {\displaystyle n} -vertex complete graph cannot be partitioned into fewer than
Graham–Pollak_theorem
Direct sum of uniform matroids
matroid. Direct sums of partition matroids are partition matroids as well. A maximum matching in a graph is a set of edges that is as large as possible
Partition_matroid
Graph-theoretic connectivity parameter
removed/components created in a decomposition of the graph in question. It is a method to compute partitions of the set of vertices and detect zones of high
Strength_of_a_graph
Bipartite graph partition with special property
In graph theory, the Dulmage–Mendelsohn decomposition is a partition of the vertices of a bipartite graph into subsets, with the property that two adjacent
Dulmage–Mendelsohn decomposition
Dulmage–Mendelsohn_decomposition
Set of edges without common vertices
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
Matching_(graph_theory)
Graph with same nodes as but complementary connections to another
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
Complement_graph
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)
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)
Bipartite graph where each node of 1st set is linked to all nodes of 2nd set
similar drawings of complete graphs three centuries earlier. A complete bipartite graph is a graph whose vertices can be partitioned into two subsets V1 and
Complete_bipartite_graph
… + n(N) Area ratio r, 0< r<1 Output: 2 partitions Cutsetsize is minimized |A|/(|A|+|B|) ≈ r Graph partition Kernighan–Lin algorithm Fiduccia; Mattheyses
Fiduccia–Mattheyses_algorithm
(proper) vertex coloring
In graph theory, a strong coloring, with respect to a partition of the vertices into (disjoint) subsets of equal sizes, is a (proper) vertex coloring in
Strong_coloring
Machine learning paradigm
for graph partitioning. EEL creates an ensemble of partitions and then uses information contained in the ensemble to find new and improved partitions. The
Extremal_Ensemble_Learning
Measurement of graph sparsity
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
Degeneracy_(graph_theory)
Object in graph theory
In the mathematical subfield of graph theory a level structure of a rooted graph is a partition of the vertices into subsets that have the same distance
Level_structure
Study of graphs as a representation of relations between discrete objects
science, and network science, network theory is a part of graph theory. It defines networks as graphs where the vertices or edges possess attributes. Network
Network_theory
Method for finding largest (or smallest) eigenvalues
nvGRAPH library introduced in CUDA 8. Sphynx, a hybrid distributed- and shared-memory-enabled parallel graph partitioner - the first graph partitioning
LOBPCG
Characterizes the height of any finite partially ordered set
clique. In the comparability graph of a partially ordered set, a clique represents a chain and a coloring represents a partition into antichains, and induced
Mirsky's_theorem
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
Complete bipartite cut in a graph
a complete bipartite graph, its cut is called a split. Thus, a split can be described as a partition of the vertices of the graph into two subsets X and
Split_(graph_theory)
Maximum number of disjoint dominating sets
In graph theory, a domatic partition of a graph G = ( V , E ) {\displaystyle G=(V,E)} is a partition of V {\displaystyle V} into disjoint sets V 1 {\displaystyle
Domatic_number
Theorem on edge-disjoint spanning trees
trees (and more generally forests) a graph can have: A graph G has t edge-disjoint spanning trees iff for every partition V 1 , … , V k ⊂ V ( G ) {\textstyle
Nash-Williams_theorem
Unrelated vertices in graphs
to the number of vertices in the graph. A vertex coloring of a graph G {\displaystyle G} corresponds to a partition of its vertex set into independent
Independent set (graph theory)
Independent_set_(graph_theory)
Decomposition of a graph into hamiltonion cycles
In graph theory, a branch of mathematics, a Hamiltonian decomposition of a given graph is a partition of the edges of the graph into Hamiltonian cycles
Hamiltonian_decomposition
Topics referred to by the same term
Oceanid and wife of Zeus Metis (software), business modeling METIS, graph partitioning software METIS, an instrument for the ~2029 Extremely Large Telescope
Metis
Logical formulation of graph properties
the mathematical fields of graph theory and finite model theory, the logic of graphs deals with formal specifications of graph properties using sentences
Logic_of_graphs
Symmetric function invariant of graphs
function invariant of graphs studied in algebraic graph theory, a branch of mathematics. It is the weight generating function for proper graph colorings, and
Chromatic_symmetric_function
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
Graph with only one possible coloring
one way to partition its vertices into k independent sets and there is no way to partition them into k − 1 independent sets. A complete graph is uniquely
Uniquely_colorable_graph
goal is to partition the edges of a given graph into two triangle-free subgraphs. It is NP-complete but fixed-parameter tractable on graphs of bounded
Monochromatic_triangle
Partition of graph into sequence of paths
In graph theory, an ear of an undirected graph G is a path P where the two endpoints of the path may coincide, but where otherwise no repetition of edges
Ear_decomposition
Method of designing specialized integrated circuits
Very-large-scale integration (VLSI) A. Kahng et al.: "VLSI Physical Design: From Graph Partitioning to Timing Closure", Springer (2022), doi:10.1007/978-3-030-96415-3
Standard_cell
On coloring the edges of graphs
degree Δ of the graph. At least Δ colors are always necessary, so the undirected graphs may be partitioned into two classes: "class one" graphs for which Δ
Vizing's_theorem
GRAPH PARTITION
GRAPH PARTITION
Female
Thai/Siamese
Thai name A-GUN means "grape."
Boy/Male
Arabic, Modern
Grape
Biblical
a grape; a knot
Boy/Male
Biblical
A grape, a knot.
Boy/Male
Hindu, Indian, Punjabi, Sikh
From Kashmir; Grape
Girl/Female
Tamil
Kaslunira | கஸà¯à®²à¯à®‚நீரா
Grape, Belonging to kashmir
Kaslunira | கஸà¯à®²à¯à®‚நீரா
Girl/Female
Indian
Grape like
Boy/Male
Hebrew, Hindu, Indian, Marathi
Grape Cluster
Boy/Male
Hindu, Indian
Efficient; Conqueror of Miseries; Bond in Affection; Capable; Mysterious; Different than Others; Smart; Most Mysterious Vastu Grah 'Rahu'; Son of Lord Buddha; Son of Goddess Durga; Truth Follower; Best of All
Girl/Female
Indian
Grape vine
Boy/Male
African, Arabic
Grape Vines
Girl/Female
Hindu
Grape, Belonging to kashmir
Girl/Female
Muslim
Grape vine
Girl/Female
Arabic, Assamese, Hindu, Indian, Kannada, Malayalam, Marathi, Muslim, Telugu
Grape
Boy/Male
Indian
Grape
Girl/Female
Muslim
Grape like
Boy/Male
Muslim
Grape
Boy/Male
Afghan, Hebrew, Indian, Parsi, Sanskrit
Grape Presser; World; Song
Boy/Male
Biblical
A grape, a knot.
Girl/Female
Afghan, Arabic, Hebrew, Indian, Muslim, Parsi, Sanskrit
Grape Presser; World; Song; Universe
GRAPH PARTITION
GRAPH PARTITION
Girl/Female
Indian
One of the Ladyguru
Girl/Female
Polish
Pearl.
Male
Russian
(Егор) Russian form of Greek Georgios, YEGOR means "earth-worker, farmer."
Female
Spanish
Spanish pet form of Hebrew Sarah, SARITA means "noble lady, princess."
Girl/Female
Indian
Cheerful, Prosperous, Happy
Girl/Female
Hindu
Dispeller of ignorance
Girl/Female
Welsh
Fair, good, holy.
Boy/Male
Hindu
The Sun, Sweet
Boy/Male
Irish American
Strong willed or wise. Also a : Hero.
Boy/Male
Gujarati, Hindu, Indian, Kannada, Parsi, Sanskrit, Sindhi, Telugu
Blazing; Very Bright
GRAPH PARTITION
GRAPH PARTITION
GRAPH PARTITION
GRAPH PARTITION
GRAPH PARTITION
n.
The cultivation of the vine; grape growing.
n.
A plant of the genus Muscari; grape hyacinth.
n.
See Grasshopper, and Frog hopper, Grape hopper, Leaf hopper, Tree hopper, under Frog, Grape, Leaf, and Tree.
n.
Grapeshot.
n.
A well-known edible berry growing in pendent clusters or bunches on the grapevine. The berries are smooth-skinned, have a juicy pulp, and are cultivated in great quantities for table use and for making wine and raisins.
a.
Resembling a grape.
n.
A variety of shaddock, called also grape fruit.
n.
A grape, or a bunch of grapes.
n.
A mangy tumor on the leg of a horse.
n.
A grape of many varieties and colors.
n.
The plant which bears this fruit; the grapevine.
a.
Full of small kernels like a grape.
a.
Composed of, or resembling, grapes.
n.
A grape dried in the sun; a raisin.
n.
A sort of grape.
n.
A seed of the grape.
n.
A white grape, esteemed for the table.
n.
The Hartford grape, a variety of grape first raised at Hartford, Connecticut, from the Northern fox grape. Its large dark-colored berries ripen earlier than those of most other kinds.