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Maximal subgraph whose vertices can reach each other
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
Component_(graph_theory)
Basic concept of graph theory
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 need
Connectivity_(graph_theory)
Partition of a graph whose components are reachable from all 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
Strongly_connected_component
Topics referred to by the same term
component may refer to: Connected component (graph theory), a set of vertices in a graph that are linked to each other by paths Connected component (topology)
Connected_component
Trail in which only the first and last vertices are equal
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
Cycle_(graph_theory)
Edge whose deletion would disconnect a graph
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
Bridge_(graph_theory)
Large connected component of a random graph
network theory, a giant component is a connected component of a given random graph that contains a significant fraction of the entire graph's vertices
Giant_component
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
Tree graph with one central node and leaves of length 1
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
Star_(graph_theory)
Graph generated by a random process
The theory of random graphs lies at the intersection between graph theory and probability theory. From a mathematical perspective, random graphs are used
Random_graph
Maximal biconnected subgraph
In graph theory, a biconnected component or block (sometimes known as a 2-connected component) is a maximal biconnected subgraph. Any connected graph decomposes
Biconnected_component
Graph algorithm
strongly connected components algorithm is an algorithm in graph theory for finding the strongly connected components (SCCs) of a directed graph. It runs in
Tarjan's strongly connected components algorithm
Tarjan's_strongly_connected_components_algorithm
Graph whose biconnected components are all cliques
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)
Block_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
Two closely related models for generating random graphs
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
Erdős–Rényi_model
Topics referred to by the same term
multiple values or color components Component (group theory), a quasi-simple subnormal sub-group Connected component (graph theory), a maximal connected
Component
Topological space that is connected
Q {\displaystyle \mathbb {Q} } ). Mathematics portal Connected component (graph theory) – Maximal subgraph whose vertices can reach each otherPages displaying
Connected_space
discrete and Euclidean geometries, graph theory, group theory, mathematical logic, number theory, set theory, Ramsey theory, dynamical systems, and partial
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Type of graph
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
Biconnected_graph
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
Trail in a graph that visits each edge once
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)
Eulerian_path
Graph defined from a mathematical group
geometric group theory. The structure and symmetry of Cayley graphs make them particularly good candidates for constructing expander graphs. Let G {\displaystyle
Cayley_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
Study of graphs as a representation of relations between discrete objects
science, network theory is a part of graph theory. It defines networks as graphs where the vertices or edges possess attributes. Network theory analyses these
Network_theory
Graphical representation of energy flows in physical systems
variables are transmitted by bonds which connect bond graph components. Bond graph components are also based on analogies and, using the electrical and
Bond_graph
Characteristic of undirected graphs
matroid theory of graphs the rank of an undirected graph is defined as the number n − c, where c is the number of connected components of the graph. Equivalently
Rank_(graph_theory)
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
Assigning directions to the edges of an undirected graph
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
Orientation_(graph_theory)
Study of graphs defined by geometric means
Geometric graph theory in the broader sense is a large and amorphous subfield of graph theory, concerned with graphs defined by geometric means. In a stricter
Geometric_graph_theory
Mathematical theory on behavior of connected clusters in a random graph
random graphs Fractal – Infinitely detailed mathematical structure Giant component – Large connected component of a random graph Graph theory – Area of
Percolation_theory
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
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
Mathematical concept
Connected component (graph theory) Connected sum Cross-link Network Scale-free network Simply connected Small-world network Strongly connected component Totally
Connectedness
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)
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
Matrix representation of a graph
In the mathematical field of graph theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix, or discrete Laplacian
Laplacian_matrix
Length of shortest path between two nodes of a graph
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
Distance_(graph_theory)
the mathematics of infinite graphs, an end of an undirected graph represents, intuitively, a direction in which the graph extends to infinity. Ends may
End_(graph_theory)
Undirected, connected, and acyclic graph
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
Tree_(graph_theory)
Bijection between the vertex set of two graphs
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
Graph_isomorphism
Measurement of graph sparsity
In graph theory, a k-degenerate graph is an undirected graph in which every non-empty subgraph has at least one vertex of degree at most k {\displaystyle
Degeneracy_(graph_theory)
Method of graph decomposition
In graph theory, a bramble for an undirected graph G is a family of connected subgraphs of G that all touch each other: for every pair of disjoint subgraphs
Bramble_(graph_theory)
Form taken by the network of interconnections of a circuit
of graph theory. Standard graph theory can be extended to deal with active components and multi-terminal devices such as integrated circuits. Graphs can
Circuit_topology_(electrical)
Algorithmic application of graph theory
application of graph theory, where subsets of connected components are uniquely labeled based on a given heuristic. Connected-component labeling is not
Connected-component_labeling
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:
Nullity_(graph_theory)
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
Map_(graph_theory)
Visual technique in topological graph theory
topological graph theory, a ribbon graph is a way to represent graph embeddings, equivalent in power to signed rotation systems and graph-encoded maps
Ribbon_graph
Overview of and topical guide to algorithms
Borůvka's algorithm Connected component (graph theory) Strongly connected component Tarjan's strongly connected components algorithm Maximum flow problem
Outline_of_algorithms
On the number of spanning trees in a graph
mathematical field of graph theory, Kirchhoff's theorem or Kirchhoff's matrix tree theorem is a theorem about the number of spanning trees in a graph. It states
Kirchhoff's_theorem
Family of cubic graphs formed from regular and star polygons
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
Generalized_Petersen_graph
Graph with at most one cycle per component
In graph theory, a pseudoforest is an undirected graph in which every connected component has at most one cycle. That is, it is a system of vertices and
Pseudoforest
Type of game defined in mathematics
In combinatorial game theory, a branch of mathematics, a hot game is one in which each player can improve their position by making the next move. By contrast
Hot_game
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)
1990 book by Gerhard Ringel and Nora Hartsfield
Pearls in Graph Theory: A Comprehensive Introduction is an undergraduate-level textbook on graph theory by Nora Hartsfield and Gerhard Ringel. It was
Pearls_in_Graph_Theory
Graph with sign-labeled edges
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
Signed_graph
Representation of a mathematical function
for details. A graph of a function is a special case of a relation. In the modern foundations of mathematics, and, typically, in set theory, a function is
Graph_of_a_function
Square matrix used to represent a graph or network
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
Adjacency_matrix
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
Recursively splitting a graph into subsets of nodes
In graph theory, the modular decomposition is a decomposition of a graph into subsets of vertices called modules. A module is a generalization of a connected
Modular_decomposition
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
Characterization of graphs with perfect matchings
mathematical discipline of graph theory, the Tutte theorem, named after William Thomas Tutte, is a characterization of finite undirected graphs with perfect matchings
Tutte's theorem on perfect matchings
Tutte's_theorem_on_perfect_matchings
Index of articles associated with the same name
(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
Cyclic_graph
Tree which includes all vertices of a graph
of graph theory, a spanning tree T of an undirected graph G is a subgraph that is a tree which includes all of the vertices of G. In general, a graph may
Spanning_tree
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 modeling collaboration in a social network
Graph theory – Area of discrete mathematics Odda, Tom (1979). "On properties of a well-known graph or what is your Ramsey number? Topics in graph theory"
Collaboration_graph
Graphical representation of a computer program or algorithm
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
Control-flow_graph
Planar graph with 4 nodes and 5 edges
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
Diamond_graph
Operation combining two oriented knots
of mathematics that studies knots is known as knot theory and has many relations to graph theory. A knot is an embedding of the circle (S1) into three-dimensional
Knot_(mathematics)
Visualization of node-link graphs
Graph drawing is an area of mathematics and computer science combining methods from geometric graph theory and information visualization to derive two-dimensional
Graph_drawing
Computer science algorithm
can be used to solve many problems in graph theory, for example: finding all vertices within one connected component; Cheney's algorithm; finding the shortest
Graph_traversal
Intersection graph of unit intervals on the real line
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
Indifference_graph
Directed graph where each vertex pair has one arc
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
Tournament_(graph_theory)
Measure of whether or not a graph has a "bottleneck"
Laplacian matrix of the graph. The Cheeger inequality is a fundamental result and motivation for spectral graph theory. Spectral graph theory Algebraic connectivity
Cheeger constant (graph theory)
Cheeger_constant_(graph_theory)
Method of graph decomposition
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
Haven_(graph_theory)
Graph made from disjoint union of complete graphs
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
Cluster_graph
Trees with additional directed half edges
planar graphs, blossom trees are trees with additional directed half edges. Each blossom tree is associated with an embedding of a planar graph. Blossom
Blossom_tree_(graph_theory)
Representation of a graph's triconnected components
In graph theory, a branch of mathematics, the triconnected components of a biconnected graph are a system of smaller graphs that describe all of the 2-vertex
SPQR_tree
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
Copy of a directed graph with redundant edges removed
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
Transitive_reduction
Mathematical graph theorem
mathematical discipline of graph theory, Petersen's theorem, named after Julius Petersen, is one of the earliest results in graph theory and can be stated as
Petersen's_theorem
Physical simulation to visualize graphs
about graph theory such as planarity. Force-directed graph drawing algorithms assign forces among the set of edges and the set of nodes of a graph drawing
Force-directed_graph_drawing
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
Academic field
foundation of graph theory, a branch of mathematics that studies the properties of pairwise relations in a network structure. The field of graph theory continued
Network_science
Deleting a graph edge and merging its nodes
In graph theory, an edge contraction is an operation that removes an edge from a graph while simultaneously merging the two vertices that it previously
Edge_contraction
Recursively-formed graph with two terminal vertices
In graph theory, series–parallel graphs are graphs with two distinguished vertices called terminals, formed recursively by two simple composition operations
Series–parallel_graph
spectral graph theory, distributed computing, symbolic dynamics, graph neural networks, and category theory, under different names such as graph divisor
Fibrations_of_graphs
Theorem about infinite graphs
minors, which became an important component of the algorithmic theory of bidimensionality. A ray, in an infinite graph, is a semi-infinite path: a connected
Halin's_grid_theorem
Mixing property of Markov chains and graphs
In theoretical computer science, graph theory, and mathematics, the conductance is a parameter of a Markov chain that is closely tied to its mixing time
Conductance_(graph_theory)
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
Moral_graph
Directed graph representing a Boolean expression
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
Implication_graph
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
Rooted_graph
Graph which remains connected when k or fewer nodes removed
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
Vertex_connectivity
Mathematical theory for sol–gel processes
Random graph theory of gelation is a mathematical theory for sol–gel processes. The theory is a collection of results that generalise the Flory–Stockmayer
Random graph theory of gelation
Random_graph_theory_of_gelation
Second-smallest eigenvalue of a graph Laplacian
connected graph. This is a corollary to the fact that the number of times 0 appears as an eigenvalue in the Laplacian is the number of connected components in
Algebraic_connectivity
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
Graph of n vertices with a perfect matching for every subgraph of n-1 vertices
In graph theory, a mathematical discipline, a factor-critical graph (or hypomatchable graph) is a graph with an odd number of vertices in which deleting
Factor-critical_graph
In graph theory, the corona product of graphs G and H, denoted G ∘ H {\displaystyle G\circ H} , can be obtained by taking one copy of G, called the center
Corona_product
Graph-theoretic connectivity parameter
In graph theory, the strength of an undirected graph corresponds to the minimum ratio of edges removed/components created in a decomposition of the graph
Strength_of_a_graph
In graph theory, Berge's theorem states that a matching M in a graph G is maximum (contains the largest possible number of edges) if and only if there
Berge's_theorem
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
COMPONENT GRAPH-THEORY
COMPONENT GRAPH-THEORY
Boy/Male
Indian
Grape
Boy/Male
Arabic, Muslim
Competent
Boy/Male
Arabic, Muslim
Competent
Boy/Male
Arabic, Muslim
Competent
Boy/Male
Arabic, Muslim
Competent
Girl/Female
Arabic, Assamese, Hindu, Indian, Kannada, Malayalam, Marathi, Muslim, Telugu
Grape
Girl/Female
Muslim
Opponent
Girl/Female
Arabic, Muslim
Opponent
Girl/Female
Indian
Competent
Boy/Male
Muslim
Competent
Girl/Female
Muslim
Grape like
Boy/Male
Muslim
Grape
Boy/Male
Anglo Saxon
Competent.
Boy/Male
Indian, Sanskrit
Competent
Girl/Female
Muslim
Grape vine
Girl/Female
Indian
Grape like
Boy/Male
Hindi
Competent.
Boy/Male
Arabic, Modern
Grape
Girl/Female
Indian
Competent.
Girl/Female
Indian
Grape vine
COMPONENT GRAPH-THEORY
COMPONENT GRAPH-THEORY
Male
Welsh
Welsh legend name of the magician who guided the destiny of King Arthur, derived from Celtic Mori-dunum, MYRDDIN means "sea fort."Â Mori-dunum was a place in Wales later called Carmarthen. Because of its close resemblance to the French word merde, meaning "excrement," the name was changed from Myrddin to Merlin.Â
Female
Russian
(ÐнжелиÌна) Russian form of Latin Angelina, ANZHELINA means "angel, messenger."
Girl/Female
Muslim/Islamic
This was the name of the daughter of Jafar Mansoor and the wife of Khalifah Haroon Rasheed
Girl/Female
American, Australian, British, English, French, Greek
Maiden
Boy/Male
Hindu, Indian
Warrior of the World
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malay, Tamil
Dearer to Goddess
Girl/Female
Tamil
Nature
Boy/Male
French
Desire.
Surname or Lastname
English (chiefly Northumbria)
English (chiefly Northumbria) : occupational name for a tender of animals, normally a cowherd or shepherd, from Middle English herde + man ‘man’. The surname is also found in Ireland, where it dates back to around the 14th century.Scottish : status name from Old English hīredman ‘retainer’, denoting a member of a lord’s household and followers, the hīred.German (Herdmann) : occupational name for a tender of animals (see Herder).
Boy/Male
Assamese, Hindu, Indian, Kannada, Marathi, Tamil, Telugu
God's Grace; Gods Blessing
COMPONENT GRAPH-THEORY
COMPONENT GRAPH-THEORY
COMPONENT GRAPH-THEORY
COMPONENT GRAPH-THEORY
COMPONENT GRAPH-THEORY
n.
The separation of an aggregate body into its component parts.
v. t.
Serving, or helping, to form; composing; constituting; constituent.
n.
An opponent; an enemy.
a.
Entering as, or forming, an ingredient or component part.
n.
A constituent part; an ingredient.
a.
Rightfully or properly belonging; incident; -- followed by to.
a.
Resembling a grape.
n.
An opponent.
n.
The principal component part of a thing.
a.
Incapable of being resolved; not separable into component parts.
a.
Serving to form, compose, or make up; elemental; component.
n.
A component part of compound medicine; a simple.
n.
the residual AC component in the DC current output from a rectifier, expressed as a percentage of the steady component of the current.
n.
A seed of the grape.
n.
The quality or state of being an ingredient or component part.
n.
One of the component segments of the body of an animal.
n.
A sort of grape.
a.
Answering to all requirements; adequate; sufficient; suitable; capable; legally qualified; fit.
a.
Alt. of Compone