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joined by lines or curves for the edges. The edges may be directed or undirected. For example, if the vertices represent people at a party, and there is...

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

acyclic graphs. At its simplest, DOT can be used to describe an undirected graph. An undirected graph shows simple relations between objects, such as reciprocal...

matrix is a (0,1)-matrix with zeros on its diagonal. If the graph is undirected (i.e. all of its edges are bidirectional), the adjacency matrix is symmetric...

which encodes the relation of vertex-vertex pairs. In graph theory an undirected graph has two kinds of incidence matrices: unoriented and oriented. The...

encode and the factorization of the distribution that they induce. The undirected graph shown may have one of several interpretations; the common feature...

edges (also called arcs, links, or lines). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs...

shortest closed path or circuit that visits every edge of an (connected) undirected graph at least once. When the graph has an Eulerian circuit (a closed...

for an undirected graph requires about 2⋅(32/8)|E| = 8|E| bytes of space, where |E| is the number of edges of the graph. Noting that an undirected simple...

path between every pair of vertices. An undirected graph that is not connected is called disconnected. An undirected graph G is therefore disconnected if...

circuit is called semi-Eulerian. An Eulerian trail, or Euler walk, in an undirected graph is a walk that uses each edge exactly once. If such a walk exists...

USTCON (undirected s-t connectivity), which is the problem of determining whether there exists a path between two vertices in an undirected graph, otherwise...

path problem can be defined for graphs whether undirected, directed, or mixed. The definition for undirected graphs states that every edge can be traversed...

to be undirected, in which case they correspond to Weyl groups. In this article, "Dynkin diagram" means directed Dynkin diagram, and undirected Dynkin...

instead of A), arrows, or directed lines. It differs from an ordinary or undirected graph, in that the latter is defined in terms of unordered pairs of vertices...

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 Neil Robertson. The Robertson...

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...

vertex induces an undirected tree. A polytree (also called a directed tree) is a multitree formed by orienting the edges of an undirected tree. An arborescence...

travel distance. It is also sometimes called the undirected chinese postman problem. The undirected rural postman problem (URPP) aims to minimize the...

In mathematics, a minimum bottleneck spanning tree (MBST) in an undirected graph is a spanning tree in which the most expensive edge is as cheap as possible...

the vertex numbers for the best-known graphs (as of June 2024) in the undirected degree diameter problem for graphs of degree at most 3 ≤ d ≤ 16 and diameter...

edges have a direction indicating the flow or relationship between nodes. Undirected graphs, simply referred to as graphs in NetworkX, are graphs where edges...

In 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 graph theory, the cube-connected cycles is an undirected cubic graph, formed by replacing each vertex of a hypercube graph by a cycle. It was introduced...

Unsolved problem in mathematics Does every undirected graph G {\displaystyle G} have a triangle-hitting set whose size is at most twice the number of triangles...

Moser spindle (also called the Mosers' spindle or Moser graph) is an undirected graph, named after mathematicians Leo Moser and his brother William, with...

pair ( X , E ) {\displaystyle {\left(X,E\right)}} shall be called an undirected hypergraph. Hypergraphs can be viewed as incidence structures. In particular...

algorithms (see, for example, Reingold's algorithm for connectivity in undirected graphs). As Lipton states: This alone could be important and often is...

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...

least one such path exists. Notice that, in contrast with the case of undirected graphs, d(u,v) does not necessarily coincide with d(v,u)—so it is just...

term is an "arborescence"), meaning: A directed graph, whose underlying undirected graph is a tree (any two vertices are connected by exactly one simple...

In 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...

(which is an undirected graphical model), while lower layers form a directed generative model. In a DBM all layers are symmetric and undirected. Like DBNs...

In graph theory, a bipolar orientation or st-orientation of an undirected graph is an assignment of a direction to each edge (an orientation) that causes...

algorithm to determine whether a path exists between two nodes in an undirected graph, a problem that requires O(n) extra space using typical algorithms...

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 adjacent...

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...

solves the undirected st-connectivity problem, the problem of testing whether there is a path between two given vertices in an undirected graph, using...

range of possible graph structure constellations including directed, undirected, mixed graphs, hypergraphs, and application-specific attributes. A GraphML...

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...

combinatorial mathematics, a block graph or clique tree is a type of undirected graph in which every biconnected component (block) is a clique. Block...

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...

states that every finite group is the group of symmetries of a finite undirected graph. More strongly, for any finite group G {\displaystyle G} , there...

{\displaystyle \sum _{v\in V}\deg(v)=2|E|\,} . The formula implies that in any undirected graph, the number of vertices with odd degree is even. This statement...

function of the degree distribution P ( k ) {\displaystyle P(k)} for an undirected network, then G 1 ( x ) {\displaystyle G_{1}(x)} can be defined as G 1...

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 M. Goldner...

In graph theory, the Petersen family is a set of seven undirected graphs that includes the Petersen graph and the complete graph K6. The Petersen family...

Hamiltonian decompositions have been studied both for undirected graphs and for directed graphs. In the undirected case a Hamiltonian decomposition can also be...

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

In mathematics, and more specifically in graph theory, a multigraph is a graph which is permitted to have multiple edges (also called parallel edges),...

equivalently in which the subgraph reachable from any vertex induces an undirected tree, or a partially ordered set (poset) that does not have four items...

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...

directed graphs and ( N − 1 ) ( N − 2 ) / 2 {\displaystyle (N-1)(N-2)/2} for undirected graphs, where N {\displaystyle N} is the number of nodes in the giant...

vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs...

graph-theoretic mathematics, a cycle double cover is a collection of cycles in an undirected graph that together include each edge of the graph exactly twice. For...

Here is a simple example of a labelled, undirected graph and its Laplacian matrix. We observe for the undirected graph that both the adjacency matrix and...

graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once. A Hamiltonian...

graphs. That is, it is possible to choose a direction for each edge of an undirected graph G, turning it into a directed graph that has a path from every vertex...

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 arcs) A. Consider adjacent vertices...

underlying undirected graph is a forest. In other words, if we replace its directed edges with undirected edges, we obtain an undirected graph that is...

(MRF), Markov network or undirected graphical model is a set of random variables having a Markov property described by an undirected graph. In other words...

be directed or undirected; undirected edges are also called lines and directed edges are also called arcs or arrows. In an undirected simple graph, an...

mathematical field of algebraic graph theory, the degree matrix of an undirected graph is a diagonal matrix which contains information about the degree...

graph is the intersection graph of a chord diagram. That is, it is an undirected graph whose vertices can be associated with a finite system of chords...

both undirected and bidirected (directed) settings: In undirected path coloring, the graph G {\displaystyle G} is undirected, and paths are undirected. Two...

mathematical field 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...

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...

by Raimund Seidel in 1992 for the all-pairs-shortest-path problem for undirected, unweighted, connected graphs. It solves the problem in O ( V ω log ⁡...

from the rectangular grid of the standard square lattice to an arbitrary undirected finite multigraph G = ( V , E ) {\displaystyle G=(V,E)} , a special vertex...

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...

Kruskal's algorithm finds a minimum spanning forest of an undirected edge-weighted graph. If the graph is connected, it finds a minimum spanning tree....

a class of combinatorial enumeration problems in which one must count undirected or directed graphs of certain types, typically as a function of the number...

graphs in which every edge is a bridge are exactly the forests. In every undirected graph, there is an equivalence relation on the vertices according to which...

rational or real numbers, etc. The existence of a cycle in directed and undirected graphs can be determined by whether a depth-first search (DFS) finds an...

mathematical area of graph theory, the Mycielskian or Mycielski graph of an undirected graph is a larger graph formed from it by a construction of Jan Mycielski (1955)...

approximation ratio in polynomial time. The input to the problem consists of an undirected graph with weights on its edges, and a number k. The output is a tree...

mathematical 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...

finding a deterministic logarithmic-space algorithm for st-connectivity in undirected graphs. He, along with Avi Wigderson and Salil Vadhan, won the Gödel Prize...

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

In graph theory, the Grundy number or Grundy chromatic number of an undirected graph is the largest number of colors in any greedy coloring of the graph...

cyclomatic number, circuit rank, cycle rank, corank or nullity of an undirected graph is the minimum number of edges that must be removed from the graph...

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...

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

of an undirected graph, one less than the size of the largest vertex-set in the decomposition. Width of a path decomposition of an undirected graph,...

There are variants of modular decomposition for undirected graphs and directed graphs. For each undirected graph, this decomposition is unique. This notion...

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

In combinatorial optimization, the Gomory–Hu tree of an undirected graph with capacities is a weighted tree that represents the minimum s-t cuts for all...

common ancestors algorithm Tarjan's algorithm for finding bridges in an undirected graph Tarjan's algorithm for finding simple circuits in a directed graph...

A family of simple undirected graphs defined by spectral properties...

edge-connectivity version of Menger's theorem is as follows: Let G be a finite undirected graph and x and y two distinct vertices. Then the size of the minimum...

graphs (having both directed and undirected edges). The program is solvable in polynomial time if the graph has all undirected or all directed edges. Variants...

containing at least one vertex from every cycle in a directed or undirected graph. In undirected graphs, the spanning trees are the largest acyclic subgraphs...

The arboricity of an undirected graph is the minimum number of forests into which its edges can be partitioned. Equivalently it is the minimum number of...

In the mathematical field 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...

Undirected movement by plants in response to temperature...

this result to multi-commodity flow problems. The Gomory–Hu tree of an undirected flow network provides a concise representation of all minimum cuts between...

mathematical 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...

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...

reflections). The number of undirected closed tours is half this number, since every tour can be traced in reverse. There are 9,862 undirected closed tours on a...

inequality. Formally, Feld assumes that a social network is represented by an undirected graph G = (V, E), where the set V of vertices corresponds to the people...

Unschooling may emphasize free, undirected play as a major component of children's education....

the best known algorithms for both undirected and directed graphs is a simple greedy algorithm: In the undirected case, the greedy tour is at most O(ln...

algorithm aimed at solving the election problem in generic connected undirected graph. Mega-Merger was developed by Robert Gray Gallager at MIT in 1983...

{\displaystyle n} -vertex undirected graph can be computed in time O ( n 2 ) {\displaystyle O(n^{2})} . In any graph, directed or undirected, there is a straightforward...

fields of complexity theory and graph theory. It decides if a directed or undirected graph, G, contains a Hamiltonian path, a path that visits every vertex...

often used as a form of knowledge representation. It is a directed or undirected graph consisting of vertices, which represent concepts, and edges, which...

which s belongs to the set S and t belongs to the set T. In an unweighted undirected graph, the size or weight of a cut is the number of edges crossing the...

a preorder on graphs, a distributive lattice, and a category (one for undirected graphs and one for directed graphs). The computational complexity of finding...

Undirected movement in response to touch or vibration...

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, 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...

Turing machine is a Turing machine that has a configuration graph that is undirected (that is, configuration i yields configuration j if and only if j yields...

In graph theory, a branch of mathematics, the splittance of an undirected graph measures its distance from a split graph. A split graph is a graph whose...

graph is the undirected Hasse diagram of the partially ordered set, and in the second case, the graph is simply the underlying (undirected) graph of the...

dimension is 2 for the Ising model, or for directed percolation, but 1 for undirected percolation), and above the upper critical dimension d ∗ {\displaystyle...

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

(representing tasks to be performed) may be connected by both directed and undirected edges (representing timing constraints between tasks). The two types of...

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...

adjacency matrix or Laplacian matrix. The adjacency matrix of a simple undirected graph is a real symmetric matrix and is therefore orthogonally diagonalizable;...

existence of a Hamiltonian cycle based on the degrees of the vertices in an undirected graph. It implies two other degree-based sufficient conditions, Dirac's...

{|\{e_{jk}:v_{j},v_{k}\in N_{i},e_{jk}\in E\}|}{k_{i}(k_{i}-1)}}.} An undirected graph has the property that e i j {\displaystyle e_{ij}} and e j i {\displaystyle...

Robertson–Seymour theorem (also called the graph minors theorem) states that the undirected graphs, partially ordered by the graph minor relationship, form a well-quasi-ordering...

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

abstract simplicial complexes are mathematically equivalent to simple undirected graphs: the vertex set of the complex can be viewed as the vertex set...

cluster graphs are transitively closed, and every transitively closed undirected graph is a cluster graph. The cluster graphs are the graphs for which...

An example for an undirected Graph with a vertex r and its corresponding level structure...

capacity of an s-t cut in the new sense. In the undirected edge-disjoint paths problem, we are given an undirected graph G = (V, E) and two vertices s and t...

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...

In graph theory and order theory, a comparability graph is an undirected graph that connects pairs of elements that are comparable to each other in a partial...

In mathematics, Paley graphs are undirected graphs constructed from the members of a suitable finite field by connecting pairs of elements that differ...

forces instead of energy. Useful for undirected graphs. sfdp multiscale version of fdp for the layout of large undirected graphs. twopi for radial graph layouts...

branches labeled "4" or greater are directed, while Coxeter diagrams are undirected; secondly, Dynkin diagrams must satisfy an additional (crystallographic)...

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 paper...

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

In 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...

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 of...

mathematical discipline of graph theory, the edge space and vertex space of an undirected graph are vector spaces defined in terms of the edge and vertex sets,...

Automorphisms may be defined in this way both for directed graphs and for undirected graphs. The composition of two automorphisms is another automorphism,...

problem of whether there exists a path between two vertices in a given undirected graph, is in L, showing that L = SL, since USTCON is SL-complete. One...

dismissed Cohen as a likely suspect because in the asylum his assaults were undirected, and his behaviour was wild and uncontrolled, whereas the Ripper seemed...

endpoints with previous subgraphs. According to Robbins' theorem, an undirected graph may be oriented in such a way that it becomes strongly connected...

usually called Directed Hamiltonian cycle) Undirected Hamilton circuit (Karp's name, now usually called Undirected Hamiltonian cycle) Satisfiability with...

{\displaystyle v_{t}} into the existing graph. Edges are undirected in respective undirected graphs. At time t {\displaystyle t} , vertex v t {\displaystyle...

888 trees with four unlabeled and three labeled nodes, 888 seven-node undirected graphs without isolated vertices, and 888 non-alternating knots whose...

{\displaystyle \Theta (n)} time and does not affect asymptotic performance. For undirected graphs, the algorithm can be stopped early after the k = ⌊ n − 1 2 ⌋ {\textstyle...

game on an undirected graph (that is, the edges can be traversed in both directions). Fraenkel, Scheinerman, and Ullman show that undirected vertex geography...

maximum leaf spanning tree are two closely related structures defined on an undirected graph. A connected dominating set of a graph G is a set D of vertices...

geometric graph theory, a branch of mathematics, a polyhedral graph is the undirected graph formed from the vertices and edges of a convex polyhedron. Alternatively...

In graph theory, a strong orientation of an undirected graph is an assignment of a direction to each edge (an orientation) that makes it into a strongly...

In graph theory, a folded cube graph is an undirected graph formed from a hypercube graph by adding to it a perfect matching that connects opposite pairs...

graph theory, the Fibonacci cubes or Fibonacci networks are a family of undirected graphs with rich recursive properties derived from its origin in number...

5, 0, .25], [0, 0.5, 1, 0]]) v = pagerank(M, 0.85) The PageRank of an undirected graph G {\displaystyle G} is statistically close to the degree distribution...

of a given direction and its corresponding opposite direction forms an undirected "line", sometimes called the direction line or an orientation, e.g., the...

multiple edges (also called parallel edges or a multi-edge), are, in an undirected graph, two or more edges that are incident to the same two vertices, or...

English to write the word-initial sound /n/ Complete graph (Kn), a simple undirected graph in which every pair of distinct vertices is connected by a unique...

(2003). Bethe free energy and contrastive divergence approximations for undirected graphical models. utoronto.ca (PhD thesis). University of Toronto. hdl:1807/122253...

intersection representation of them. Formally, an intersection graph G is an undirected graph formed from a family of sets S i , i = 0 , 1 , 2 , … {\displaystyle...

the friendship graph (or Dutch windmill graph or n-fan) Fn is a planar, undirected graph with 2n + 1 vertices and 3n edges. The friendship graph Fn can be...

mathematics In the mathematical field of graph theory, the Petersen graph is an undirected graph with 10 vertices and 15 edges. It is a small graph that serves as...

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

that does not allow an unbiased estimator of zero Complete graph, an undirected graph in which every pair of vertices has exactly one edge connecting...

robustness and synchronizability of networks. The algebraic connectivity of undirected graphs with nonnegative weights is a ( G ) ≥ 0 {\displaystyle a(G)\geq...

In graph theory, a Ptolemaic graph is an undirected graph whose shortest path distances obey Ptolemy's inequality, which in turn was named after the Greek...

inclusion of sets; B) each vertex belongs to exactly two edges; C) the undirected graph formed by the vertices and edges is connected. An abstract polytope...

number is the minimum number of vertices, v = R(m, n), such that all undirected simple graphs of order v, contain a clique of order m, or an independent...

disorder.[citation needed] Whereas stimming is a nonpharmacologic but undirected and sometimes harmful amelioration, directed therapy tries to introduce...

sometimes called a Brooks coloring or a Δ-coloring. For any connected undirected graph G with maximum degree Δ, the chromatic number of G is at most Δ...

a greedy algorithm that finds a minimum spanning tree for a weighted undirected graph. This means it finds a subset of the edges that forms a tree that...

1 , {\displaystyle s=s^{-1},} then it is typically represented by an undirected edge. The set S {\displaystyle S} is often assumed to be finite, especially...

Bayesian networks, and is a procedure to turn a directed graph into an undirected one. We do this because it allows for the universal applicability of the...

describe the cliques (complete subgraphs) of an undirected graph. The clique complex X(G) of an undirected graph G is an abstract simplicial complex (that...

O(V^{2})} for dense graphs. This is as fast as Prim's algorithm for an undirected minimum spanning tree. In 1986, Gabow, Galil, Spencer, and Tarjan produced...

implementation keeps track of visited nodes, and can therefore be used for undirected graphs. It can be modified to retrieve the path. procedure GBS(start,...

graph theory. It was introduced by Tarjan and Vishkin in 1984. Given an undirected tree presented as a set of edges, the Euler tour representation (ETR)...

mathematician. He is known for characterizing the degree sequences of undirected graphs and the Havel–Hakimi algorithm. It is an important contribution...

concept of contraction of an edge ( u , v ) {\displaystyle (u,v)} in an undirected graph G = ( V , E ) {\displaystyle G=(V,E)} . Informally, the contraction...

and knocks him out, breaking Legendre's mental control of his zombies. Undirected, the zombies walk forward and topple off the cliff. Legendre awakens and...

mathematics, in graph theory, the Seidel adjacency matrix of a simple undirected graph G is a symmetric matrix with a row and column for each vertex, having...

the shortest traversal of a graph with a set of vertices V, a set of undirected edges E with positive rational weights, and a set of directed arcs A with...

In graph theory, a branch of mathematics, the linear arboricity of an undirected graph is the smallest number of linear forests its edges can be partitioned...

In the mathematical field of graph theory, the Chvátal graph is an undirected graph with 12 vertices and 24 edges, discovered by Václav Chvátal in 1970...

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, 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, an odd cycle transversal of an undirected graph is a set of vertices of the graph that has a nonempty intersection with every odd cycle...

node is the head (or target or destination), but they can also contain undirected (bidirectional or reflexive) edges. Nodes and edges, collectively known...

to how a directed graph may be viewed as an orientation of an ordinary undirected graph. A symmetric directed graph (that is, a directed graph in which...

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...

onto six faces of a cube. In mathematics, the space of orientations of undirected lines in 3-dimensional space is called the real projective plane, and...

In graph theory, a subfield of mathematics, a well-colored graph is an undirected graph for which greedy coloring uses the same number of colors regardless...

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...

(2003). Bethe free energy and contrastive divergence approximations for undirected graphical models. utoronto.ca (PhD thesis). University of Toronto. hdl:1807/122253...

99-graph problem is an unsolved problem asking whether there exists an undirected graph with 99 vertices, in which each two adjacent vertices have exactly...

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

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...

Nick Shay, the man who ultimately ends up with the baseball, from his undirected existence as an executive of a waste management company in Arizona in...

guaranteed to be within 2–3% of an optimal tour. TSP can be modeled as an undirected weighted graph, such that cities are the graph's vertices, paths are the...

theory, the handshaking lemma is the statement that, in every finite undirected graph, the number of vertices that touch an odd number of edges is even...

818,272, Method for discovery of clusters of objects in an arbitrary undirected graph using a difference between a fraction of internal connections and...

Undirected movement in response to external stimuli...

determined to fund only "mission-oriented direct research, rather than basic undirected research". As AI founder John McCarthy writes "it would be a great relief...

an equitable coloring is an assignment of colors to the vertices of an undirected graph, in such a way that No two adjacent vertices have the same color...

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...

described at its Board Game Geek entry. An explicit solution for the undirected switching game was found in 1964 for any such game using matroid theory...

been studied. In the maximum independent set problem, the input is an undirected graph, and the output is a maximum independent set in the graph. If there...

is a matroid whose independent sets are the forests in a given finite undirected graph. The dual matroids of graphic matroids are called co-graphic matroids...

finding maximal cliques in an undirected graph MaxCliqueDyn maximum clique algorithm: find a maximum clique in an undirected graph Strongly connected components...

chain and the choice of the starting state. The cover time of a connected undirected graph is the cover time of the Markov chain that takes a random walk on...

G = (V, E) be a simple undirected graph and let P consist of all pairs of distinct vertices in V. Then the simple undirected graph H = (V, P \ E) is...

vertex, all edges must be loops. Such a graph is called a bouquet. For an undirected graph, the degree of a vertex is equal to the number of adjacent vertices...

In the mathematical area of graph theory, an undirected graph G is strongly chordal if it is a chordal graph and every cycle of even length (≥ 6) in G...

Kamada, Tomihisa; Kawai, Satoru (1989), "An algorithm for drawing general undirected graphs", Information Processing Letters, 31 (1), Elsevier: 7–15, doi:10...

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

respectively, find an approximately optimal maximum flow but only work in undirected graphs. In 2013 James B. Orlin published a paper describing an O ( | V...

searching for matchings, optional cliques, and stable sets in a given undirected graph. An algorithm is said to solve a search problem if, for every input...

/ σ[v] * (1 + δ[v]) if v ≠ s then CB[v] ← CB[v] + δ[v] // Halved for undirected graphs return CB The running time of the algorithm is expressed in terms...

C. or Forest F.C., a pioneer football team Forest (graph theory), an undirected graph all of whose connected components are trees Forest (name), a given...

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...

grid graph, 209 partial permutations on four elements, and 209 distinct undirected simple graphs on 7 or fewer unlabeled vertices. 209 is the smallest number...

a given undirected graph and generated by a type of graph labeling called a friendly labeling. A friendly labeling of an n-vertex undirected graph G =...

{\displaystyle (n-1)(n-2)} and for undirected graphs is ( n − 1 ) ( n − 2 ) / 2 {\displaystyle (n-1)(n-2)/2} . For example, in an undirected star graph, the center...

breadth-first search. Breadth-first search can be generalized to both undirected graphs and directed graphs with a given start node (sometimes referred...

only one cluster at a given moment. The original algorithm applies to undirected, weighted, and unweighted graphs. Chinese whispers runs in linear time...

graph theory, a branch of mathematics, the cop number or copnumber of an undirected graph is the minimum number of cops that suffices to ensure a win (i.e...

terminology prevailed. It is also possible to interpret a binary tree as an undirected, rather than directed graph, in which case a binary tree is an ordered...

In network science, a gradient network is a directed subnetwork of an undirected "substrate" network where each node has an associated scalar potential...

possible directions. Equivalently, a tournament is an orientation of an undirected complete graph. (However, as directed graphs, tournaments are not complete:...

theorem, named after William Thomas Tutte, is a characterization of finite undirected graphs with perfect matchings. It is a special case of the Tutte–Berge...

branch of mathematics, Steinitz's theorem is a characterization of the undirected graphs formed by the edges and vertices of three-dimensional convex polyhedra:...

table also indicates whether an algorithm can be used for directed or undirected networks as well as induced or non-induced subgraphs.[citation needed]...

starts with s {\displaystyle s} and ends with t {\displaystyle t} . In an undirected graph, reachability between all pairs of vertices can be determined by...

(Zero to the power of zero). If G {\displaystyle G} is an edge-weighted undirected graph, all edge weights are positive, and d ( u , v ) {\displaystyle d(u...

graph, named after Andrew Yao, is a kind of geometric spanner, a weighted undirected graph connecting a set of geometric points with the property that, for...

Turán's theorem bounds the number of edges that can be included in an undirected graph that does not have a complete subgraph of a given size. It is one...

polynomial time as an instance of the vertex-disjoint paths problem on undirected graphs. List of Nikoli puzzle types Thomas Snyder (19 November 2010)....

A gene co-expression network (GCN) is an undirected graph, where each node corresponds to a gene, and a pair of nodes is connected with an edge if there...

"eigenvalue bound." Vadhan also came up with another simplified approach to the undirected ST-connectivity problem following Reingold's breakthrough result. Also...

In graph theory, a branch of mathematics, a radio coloring of an undirected graph is a form of graph coloring in which one assigns positive integer labels...

simple: either show how a structured, regular world could arise out of undirected processes, or inject intelligence into the system. — R. J. Hankinson,...

reducible to determining if a path exist between given vertices in an undirected graph. In October 2004 it was discovered that this class is in fact equal...

cycle rank of a directed graph is closely related to the tree-depth of an undirected graph and to the star height of a regular language. It has also found...

thus the directed-graph form of a rooted tree, understood here as an undirected graph. An arborescence is also a directed rooted tree in which all edges...

independent random weights from some distribution to the edges of an undirected graph, and then constructing the minimum spanning tree of the graph. When...

of error-correcting codes. Intuitively, an expander graph is a finite, undirected multigraph in which every subset of the vertices that is not "too large"...

modeled by a network in which the vertices represent cities and the (undirected) edges represent potential freight delivery routes between pairs of cities...

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...

the 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...

In graph theory, an acyclic orientation of an undirected graph is an assignment of a direction to each edge (an orientation) that does not form any directed...

Topological ordering of directed acyclic graphs Degeneracy ordering of undirected graphs Elimination ordering of chordal graphs Order, the complexity of...

distinct elements are considered equivalent under the equality relation. An undirected graph may be associated to any symmetric relation on a set X , {\displaystyle...

takes the form of two nested polygons, a square within an octagon. The undirected graph obtained from the augmented octahedron, with or without its eight...

2 ) {\displaystyle C(p_{1}\times p_{2})=C(p_{1})+C(p_{2})} If G is an undirected graph, it can be used to define a communications channel in which the...

am not going to encourage this. Your work is not anybody else’s, and undirected chatter is the worst poisonous element in a humane society. — Aleister...

term of its number of edges. The conjecture states that if G is a simple undirected graph and L(G) its Laplacian matrix, then its eigenvalues λn(L(G)) ≤ λn−1(L(G))...

Jewish law Menachem Elon writes: Custom, because of its spontaneous and undirected nature, sometimes calls for a measure of supervision and control. At times...

geometry and geometric graph theory, a β-skeleton or beta skeleton is an undirected graph defined from a set of points in the Euclidean plane. Two points...

graph theory. For example, if A is the adjacency matrix of an n-vertex undirected graph G, and J is the all-ones matrix of the same dimension, then G is...

there is no guarantee that they may be converted into online buyers. "Undirected Information-seekers" are newcomers to a product or service. They are more...

the elements Probabilistic graphical model, which can be directed or undirected Portable Graymap File Format, a Netpbm format file format for images Pragmatic...

types of surveillance: Mass surveillance is also known as “passive” or “undirected” surveillance. [...] It is not targeted on any particular individual but...

revolution', in the Near East at least, was a long-term, gradual and undirected process, marked by threshold events, the outcome of which was by no means...

species, whether progressive goal-directed orthogenesis or Charles Darwin's undirected theory of evolution. The chain of being continued to be part of metaphysics...

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

In the mathematical field of graph theory, a snark is an undirected graph with exactly three edges per vertex whose edges cannot be colored with only three...

crossing number of complete graphs, as follows. A complete graph is an undirected graph in which every pair of vertices form the endpoints of an edge. The...

problem can also be defined on a complete undirected graph G = (V, E) as follows: Given a complete undirected graph G = (V, E) with distances d(vi, vj) ∈ N...

relation of the DAG and a strict partial order. The transitive closure of an undirected graph produces a cluster graph, a disjoint union of cliques. Constructing...

complete problems such as determining the rectilinear crossing number of an undirected graph. Each problem in ∃ R {\displaystyle \exists \mathbb {R} } inherits...

combinatorial system in which an orientation is given to the edges of a weighted undirected graph, subject to certain constraints. One can change this orientation...

with unsupervised pre-training and/or supervised fine-tuning. Unlike the undirected symmetric top layer, with a two-way unsymmetric layer for connection for...

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

governed by the connectivity or density of the network topology. In an undirected network, every edge connects two nodes such that there are 2m nodes per...

integer programming. Let G = ( V , E ) {\displaystyle G=(V,E)} be an undirected graph whose vertex set V {\displaystyle V} represents items that the farmer...

bookshops. In his essay, Forsyth makes the case for the lost pleasures of undirected browsing that cannot be achieved with an internet search. Reviewer Matthew...

In graph theory, a Pfaffian orientation of an undirected graph assigns a direction to each edge, so that certain cycles (the "even central cycles") have...

bipartite, such problems are also known as the assignment problem. Given an undirected graph G = ( V , E , w ) {\displaystyle G=(V,E,w)} with vertex set V {\displaystyle...

of the three sides of the preceding triangle. The Fibonacci cube is an undirected graph with a Fibonacci number of nodes that has been proposed as a network...

skyhooks, and the orderly world we know is the result of a blind and undirected shuffle through chaos. The eighth chapter's message is conveyed by its...

directed at particular things. People conclude that because moods are undirected they are also nonintentional i.e. they lack intentionality or aboutness...

classical definition is sufficient: a molecular graph is a connected, undirected graph which admits a one-to-one correspondence with the structural formula...

Web server overload causes Webattacker Zombie (computer science) "An Undirected Attack Against Critical Infrastructure" (PDF). United States Computer...

about room labels, recorded as 2-bit values. The goal is to reconstruct the entire layout as an undirected graph using as few expeditions as possible....

sequential algorithm for computing biconnected components in a connected undirected graph is due to John Hopcroft and Robert Tarjan (1973). It runs in linear...

translated first-person storyline, and its emphasis on player-driven undirected exploration. In 2019, the game was re-released through emulation for Windows...

preserve declining populations. Bovid hybrids may occur naturally through undirected interbreeding, traditional pastoral practices, or may be the result of...

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...

complement graph K0, a forest, and a planar graph. It may be considered undirected, directed, or even both; when considered as directed, it is a directed...

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

Cheeger constant is named after the mathematician Jeff Cheeger. Let G be an undirected finite graph with vertex set V(G) and edge set E(G). For a collection...

VLSI chip design. The FVS decision problem is as follows: INSTANCE: An (undirected or directed) graph G = ( V , E ) {\displaystyle G=(V,E)} and a positive...

In graph theory, the tree-depth of a connected undirected graph G {\displaystyle G} is a numerical invariant of G {\displaystyle G} , the minimum height...

electronic design automation of VLSI. The input to the algorithm is an undirected graph G = (V, E) with vertex set V, edge set E, and (optionally) numerical...

directed cycles Forest (graph theory), an undirected acyclic graph Polytree, a directed graph without any undirected cycles This disambiguation page lists...

on multi-core architectures. Creation and manipulation of directed or undirected graphs. Association of arbitrary information to the vertices, edges or...

particular for graph theory is used for description, with an ordinary (undirected) graph presumed to correspond to a symmetric relation, and a general endorelation...

"familiar yet unknown" will soon occur. Abductees also report feeling severe, undirected anxiety at this point even though nothing unusual has actually occurred...

can be computed in polynomial time, a problem which is #P-complete for undirected graphs. It is also used in the asymptotic enumeration of Eulerian circuits...

prove it is using the Motzkin-Straus theorem. It states that, for any undirected graph G, a certain quadratic program associated with G has a maximum that...

in Hungary. In 1932, the young Henri Cartier-Bresson, at the time an undirected photographer who catalogued his travels and his friends, saw the Munkácsi...

into the Euclidean plane without crossings, but in three dimensions, any undirected graph may be embedded into space without crossings. However, a spatial...

theorem may be obtained from Woodall by replacing every edge in a given undirected graph by a pair of directed edges. A closely related theorem by Meyniel...

problème des labyrinthes, is a method for traversing a maze or connected undirected graph with no prior knowledge of the maze layout. It is similar to Trémaux’s...

set in a graph is necessarily also a minimal dominating set. Given an undirected graph G = (V, E), a subset of vertices D ⊆ V {\displaystyle D\subseteq...

reconstruction conjecture reduces to the reconstruction conjecture in the undirected case, because if all the vertex-deleted subgraphs of two graphs are isomorphic...

States. June, 2008. ISBN 978-0262026499 Reingold, Omer (3 May 2008). "Undirected Connectivity in Log-Space". omereingold.files.wordpress.com. Archived...

potential prey knows it's been seen and stands still to avoid detection, undirected leaps occur in the vicinity of the prey. As a result, the prey will then...

orientation it finds is called a Pfaffian orientation. Let G = (V, E) be an undirected graph with adjacency matrix A. Define PM(n) to be the set of partitions...

pace and tone are uncertain, and Lewis's performance is embarrassingly undirected." The film has been released twice on Region 1 DVD, on 8 July 2003 and...

from the movie Barnyard and its TV series Goldner–Harary graph, simple undirected graph with 11 vertices and 27 edges Goldner String Quartet, Australian...

field, a set of random variables having a Markov property described by an undirected graph Markov's inequality, a probabilistic upper bound Markovian (disambiguation)...

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

the mathematical 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...

I_{2}(6)\cong G_{2}} ). This can be proven by comparing the restrictions on (undirected) Dynkin diagrams with the restrictions on Coxeter diagrams of finite groups:...

In graph theory, a panconnected graph is an undirected graph in which, for every two vertices s and t, there exist paths from s to t of every possible...

actors i.e. movie stars. The co-stardom network can be represented by an undirected graph. Nodes correspond to the movie star actors and two nodes are linked...

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...

key class of such problems stems from the fact that, like adjacency in undirected graphs, intersection of sets (or, more precisely, non-disjointness) is...

}\sigma _{i}\sigma _{j}.} A subset S of the vertex set V(G) of a weighted undirected graph G determines a cut of the graph G into S and its complementary subset...

graceful graph on 14 nodes has exactly 68 edges. There are 68 different undirected graphs with six edges and no isolated nodes, 68 different minimally 2-connected...

weights w i j {\displaystyle w_{ij}} for all edges in an incomplete, undirected, weighted graph. The problem can be solved in polynomial time. One method...

then neither contains the other. Coherence spaces are in bijection with undirected graphs whose vertices are tokens. Given a coherence space A {\displaystyle...

leaned towards the abstract and esoteric. Emphasising free association and undirected coincidence between music and motif, Kilbey declined to define their meanings...

ignore hydrogen atoms ("hydrogen suppressed") and defined for connected undirected molecular graphs only. More sophisticated topological indices also take...

mean the common descent of all life on earth from a single ancestor via undirected mutation and natural selection – that's a textbook definition of neo-Darwinism –...

random fields, also known as undirected graphical models are common representations for this problem. Given an undirected graph G = (V, E), a set of random...

which one vertex has been distinguished as the root. Both directed and undirected versions of rooted graphs have been studied, and there are also variant...

In metric graph theory, a convex subgraph of an undirected graph G is a subgraph that includes every shortest path in G between two of its vertices. Thus...

formulation of the union-closed sets conjecture uses graph theory. In an undirected graph, an Independent set is a set of vertices no two of which are adjacent...

represented by the diagrams, with network nodes as vertices and connections as undirected or direct edges (depending on the type of connection). The logical network...

protect a crowd of people or to supercharge her power reserves. Left undirected, Dazzler's light will radiate from her body in all directions, producing...

bifurcation ratios. It is a dimensionless number. The pathwidth of an arbitrary undirected graph G may be defined as the smallest number w such that there exists...

an algorithm that maintains the minimum spanning forest of a weighted, undirected graph, subject to edge deletions and insertions, in O ( n 1 / 2 ) {\displaystyle...

G4 ANTLR4 grammar ANTLR4 G6 Graph6 graph data format. Used for storing undirected graphs. GB GenBank molecular biology format. GBK same as GB GBR Gerber...

application of homological methods to graph theory, Lovász proved both the undirected and directed versions of a conjecture of András Frank: Given a k-connected...

{\displaystyle n} nodes. However, the size of the set of possible networks for an undirected network (simple graph) of size n {\displaystyle n} is 2 n ( n − 1 ) /...

In the mathematical area of graph theory, a triangle-free graph is an undirected graph in which no three vertices form a triangle of edges. Triangle-free...

During the Reserve Period. Goldfrank published her memoirs, Notes on an Undirected Life, in 1978. Notes on Two Pueblo Feasts. American Anthropologist 25...

The constraint composite graph is a node-weighted undirected graph associated with a given combinatorial optimization problem posed as a weighted constraint...

target assignment problem Constraint composite graph – Node-weighted undirected graph associated with a given combinatorial optimization problem Schrijver...

GET in 2022, bioethicist Florence Ashley argued that its framing as an undirected exploration of underlying psychological issues bore similarities to conversion...

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...

number n d , k {\displaystyle n_{d,k}} of vertices in a finite simple undirected graph of maximum degree at most d {\displaystyle d} and diameter at most...

simple: either show how a structured, regular world could arise out of undirected processes, or inject intelligence into the system. This was how Aristotle…...

formulated it in his 2007 doctoral dissertation. The degeneracy of an undirected graph G is the smallest number d such that every non-empty subgraph of...

mathematical field of graph theory, the Robertson–Wegner graph is a 5-regular undirected graph with 30 vertices and 75 edges named after Neil Robertson and Gerd...

mathematical 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,...

edges are undirected, a generalisation of knot diagrams. Compact closed categories with 4-dimensional diagrams where the edges are undirected, a generalisation...

graph theory, the Harries graph or Harries (3-10)-cage is a 3-regular, undirected graph with 70 vertices and 105 edges. The Harries graph has chromatic...

image segmentation in computer vision. CRFs are a type of discriminative undirected probabilistic graphical model. Lafferty, McCallum and Pereira define a...

3n-{\sqrt {12n-3}}\right\rfloor } . It is NP-hard to test whether a given undirected planar graph can be realized as a matchstick graph. More precisely, this...

this sense, the Hopfield network can be formally described as a complete undirected graph G = ⟨ V , f ⟩ {\displaystyle G=\langle V,f\rangle } , where V {\displaystyle...

In graph theory, a branch of mathematics, a squaregraph is a type of undirected graph that can be drawn in the plane in such a way that every bounded face...

polynomial-time approximation scheme for computing the permanent. For undirected d-regular graphs G {\displaystyle G} without edge weights, the conductance...

In the mathematical area of graph theory, an undirected graph G is dually chordal if the hypergraph of its maximal cliques is a hypertree. The name comes...

graph). In the case of a simple graph (a network in which at most one (undirected) edge exists between each pair of vertices, and in which no vertices connect...

as "riotous", with the connotation of being disorganized, spontaneous, undirected, and undisciplined. He wrote that, on the contrary, such riots involved...

In graph theory, a k-tree is an undirected graph formed by starting with a (k + 1)-vertex complete graph and then repeatedly adding vertices in such a...

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...

is named after Herbert Fleischner, who published its proof in 1974. An undirected graph G {\displaystyle G} is Hamiltonian if it contains a cycle that touches...

Neumann problems. If the discrete coordinate system is interpreted as an undirected graph in the unit disc, it can be considered as a model for an electrical...

nodes, properties and edges. The edges can either be directed or undirected. In an undirected graph, an edge connecting two nodes has a single meaning. In...

1 {\displaystyle r=-1} the network is completely disassortative. For undirected networks, the assortativity coefficient can be written as r = ∑ j , k...

distributed at random. The value of the modularity for unweighted and undirected graphs lies in the range [ − 1 / 2 , 1 ] {\displaystyle [-1/2,1]} . It...

roles, sometimes in conjunction with other children or adult caregivers. Undirected play allows children to learn how to work in groups, to share, to negotiate...

In graph theory, a branch of mathematics, a cycle basis of an undirected graph is a set of simple cycles that forms a basis of the cycle space of the graph...

the underlying undirected graph of the quiver is a (finite) Dynkin diagram) nor a Euclidean quiver (i.e., the underlying undirected graph of the quiver...

algebraic analogs for the Milnor invariants. A linkless embedding of an undirected graph is an embedding into three-dimensional space such that every two...

of a recurrence plot can be considered as the adjacency matrix of an undirected and unweighted network. This allows for the analysis of time series by...

coefficient, as follows: Let G = ( V , E ) {\displaystyle G=(V,E)} be an undirected simple graph (i.e., a graph having no self-loops or multiple edges) with...

for multilayer learning architectures. An RBM can be represented by an undirected bipartite graph consisting of a group of binary hidden variables, a group...

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 graph...

that represents the incidence relation between vertices and edges of an undirected graph. The incidence poset of a graph G has an element for each vertex...

is commonly proven with a double counting argument states that every undirected graph contains an even number of vertices of odd degree. That is, the...

Connectome Project data Human Macroscopic, up to 1015 nodes directed and undirected graphs in anatomically annotated GraphML format Healthy No Braininfo Atlas...

A certain number of pebbles are distributed among the vertices of an undirected graph; the goal is to move at least one to a particular target vertex...

dichotomy at a time to or from this set of dichotomies. Moreover, the undirected graph that has the weak orderings as its vertices, and these moves as...

theory, a subfield of abstract algebra, a cycle graph of a group is an undirected graph that illustrates the various cycles of that group, given a set of...

in O(log2 n) deterministic space. The same problem for undirected graphs is called undirected s-t connectivity and was shown to be in L by Omer Reingold...

MaxCliqueDyn algorithm is an algorithm for finding a maximum clique in an undirected graph. MaxCliqueDyn is based on the MaxClique algorithm, which finds a...

the directed linear sequence of finite groups constructed above by an undirected graph ( V , E ) {\displaystyle (V,E)} of vertexes and edges. At each vertex...

independence sequence a 1 , … , a m {\displaystyle a_{1},\dots ,a_{m}} of an undirected graph where m is the maximal order of any independent set, where a i {\displaystyle...

as autonomous, "self-determinative" independently of human action, and undirected in its growth, technology in a time of Technopoly actively eliminates...

telling." But, the review also said the film's "[a]ppealing tale of an undirected army brat proving himself worthy of the most exceptional girl in high...

The algorithm suggested by Gallager, Humblet, and Spira for general undirected graphs has had a strong impact on the design of distributed algorithms...

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...

linear-time algorithm for the single-source shortest paths problem in undirected graphs (Thorup, 1999). With Mihai Pătraşcu he has shown that simple tabulation...

algorithm is a recursive algorithm to solve the minimum cut problem in undirected weighted graphs with non-negative weights. It was proposed by Mechthild...

Bipartite graphs may be characterized in several different ways: An undirected graph is bipartite if and only if it does not contain an odd cycle. A...

Empire. Some of it was directed against the government, while some was undirected. It included terrorism, worker strikes, peasant unrests, and military...

independent sets of the graph. Formally, the independence complex of an undirected graph G, denoted by I(G), is an abstract simplicial complex (that is,...

directions of the edges are ignored and the NNG is defined instead as an undirected graph. However, the nearest neighbor relation is not a symmetric one,...

organism. Some evolutionary biologists, on the other hand, view it as an undirected emergent property of the ecosystem: as each individual species pursues...

located in. However, this can be further generalized as follows: given an undirected, positively weighted graph and a target vertex, the algorithm learns upon...

union of unit squares in the plane, has a domino tiling. He forms an undirected graph that has as its vertices the points (x,y,z) in the three-dimensional...

probability. For the purposes of defining the crossing number, a drawing of an undirected graph is a mapping from the vertices of the graph to disjoint points in...

cube is a hypercube graph. According to Ramsey's theorem, every n-vertex undirected graph has either a clique or an independent set of size logarithmic in...

that govern conditional independence in probability theory is shared by undirected graphs. Variables are represented as nodes in a graph in such a way that...

Schnyder, who published its proof in 1989. The incidence poset P(G) of an undirected graph G with vertex set V and edge set E is the partially ordered set...

probability β and edges added with probability α<<β. Based loosely on the undirected protein network model of Sole et al. Vazquez proposed a growth model based...

focused primarily within the horizontal dimension, it may become loose and undirected. When it is directed and controlled in both dimensions or focused primarily...

Undirected unit-distance graph requiring four colors...

In graph theory, the (a, b)-decomposition of an undirected graph is a partition of its edges into a + 1 sets, each one of them inducing a forest, except...

In graph theory, a branch-decomposition of an undirected graph G is a hierarchical clustering of the edges of G, represented by an unrooted binary tree...

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...

are from the same edge type. It supports both directed edges as well as undirected. One of its main characteristics is its performance storage and retrieval...

well as those experiencing mania. Dereistic means: away from reality, undirected fantasy thinking. Carl Jung wrote, "This is the basic activity of psychic...

childhood. But I just can't go into it. I think I had a lot of energy and undirected need so I just kind of rebelled in a general fashion. I got myself in...

always at least 90 degrees.) No edge if the vectors are orthogonal, An undirected single edge if they make an angle of 120 degrees, A directed double edge...

silent meditation and contemplation. Normally all retreats are silent and undirected. The Big Sur International Marathon is an annual marathon that begins...

Here χ ( G ) {\displaystyle \chi (G)} denotes the chromatic number of an undirected finite graph G {\displaystyle G} . The inequality χ(G × H) ≤ min {χ(G)...

they are adjacent in G {\displaystyle G} . The same definition works for undirected graphs, directed graphs, and even multigraphs. The induced subgraph G...

mathematical field of graph theory, the Harries–Wong graph is a 3-regular undirected graph with 70 vertices and 105 edges. The Harries–Wong graph has chromatic...

gives moves for the 8-disk puzzle. The game can be represented by an undirected graph, the nodes representing distributions of disks and the edges representing...

inequalities h < r ≤ ch + 1. Radon theorem for graphs. In an arbitrary undirected graph, one may define a convex set to be a set of vertices that includes...

uses deprecated parameter |citeseerx= (help) Reingold, Omer (2008), "Undirected connectivity in log-space", J. ACM, 55 (4): 1–24, doi:10.1145/1391289...

readiness to attack, as well as building spirit and stamina. Ji-geiko (地稽古) Undirected practice where the kendōka tries all that has been learned during practice...

weights taken from a given commutative ring. In the meantime, for an undirected weighted graph the sum of the products of the edge weights of its Hamiltonian...

unsolved problems in mathematics In graph theory, the Henson graph Gi is an undirected infinite graph, the unique countable homogeneous graph that does not contain...

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...

In 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...

In the mathematical field of graph theory, a Descartes snark is an undirected graph with 210 vertices and 315 edges. It is a snark, a graph with three...

graph (also called the bowtie graph and the hourglass graph) is a planar, undirected graph with 5 vertices and 6 edges. It can be constructed by joining 2...

sphere with the antipodes identified. For example, if N = 2, the axes are undirected lines through the origin in the plane. In this case, each axis cuts the...

computer science, a shortest-path tree rooted at a vertex v of a connected, undirected graph G is a spanning tree T of G, such that the path distance from root...

elements and their adjacencies are described by the vertices and edges of an undirected graph, the polarities of their bonds can be described by orienting this...

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...

vertices. In the above definition a graph is understood to be a finite undirected simple graph. However, the notion of labeling may be applied to all extensions...

1987 Korel, B., Laski, J., Dynamic program slicing, 1988 Kamada, T., Kawai, S., An algorithm for drawing general undirected graphs, 1989 Official website...

include inferior graphics and interface, simpler trade and diplomacy, undirected research, a lack of safeguards to prevent players from building more factories...

{\displaystyle B_{m}} , for an integer parameter m {\displaystyle m} , is an undirected graph with one vertex and m {\displaystyle m} edges, all of which are...

dismissed Cohen as a likely suspect because in the asylum his assaults were undirected, and his behaviour was wild and uncontrolled, whereas the Ripper seemed...

connections crossing each other and resulting in a short circuit. To an undirected graph we may associate an abstract simplicial complex C with a single-element...

algorithm is an enumeration algorithm for finding all maximal cliques in an undirected graph. That is, it lists all subsets of vertices with the two properties...

h_{3}\sqcup e_{5}} . One may use ZDDs to represent simple paths in an undirected graph. For example, there are 12 ways to go from the upper left corner...

be shown to be total by an application of the handshaking lemma: any undirected graph that has a vertex whose degree is an odd number must have some other...

An undirected graph with adjacency matrix: [ 1 1 0 1 0 1 0 1 0 ] . {\displaystyle {\begin{bmatrix}1&1&0\\1&0&1\\0&1&0\end{bmatrix}}.}...

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 and there is...

matroid is a matroid that describes the number of degrees of freedom of an undirected graph with rigid edges of fixed lengths, embedded into Euclidean space...

and localised and for months remained chaotic and uncoordinated, if not undirected". Husayni lacked the resources to mount a full-scale assault on the Yishuv...

easy to see that a matroid is also an interval greedoid. Consider an undirected graph G. Let the ground set be the edges of G and the feasible sets be...

(nodes) and edges (connections between nodes). Graphs can be directed or undirected, and they can have cycles or be acyclic. Graph traversal algorithms include...

possible. An example is the problem of computing the arboricity of an undirected graph, the minimum number of forests needed to cover all of its edges...

In graph theory, an interval graph is an undirected graph formed from a set of intervals on the real line, with a vertex for each interval and an edge...

problem can be translated into a problem in graph theory by considering an undirected bipartite graph that has a vertex for each row and column of the given...

selected edge set are both at most one, and the graphic matroid of the undirected graph formed by forgetting the edge orientations in G, ensuring that the...

will connect the shorter distances. The links in the network will be undirected if the proximities are symmetrical for every pair of entities. Symmetrical...

weights. ← same. no lateral connections within a layer. top layer is undirected, symmetric. other layers are 2-way, asymmetric. 3-layers: asymmetric weights...

first-order sentence in the logic of graphs can be realized by a finite undirected graph. Trakhtenbrot's theorem - Finite satisfiability is undecidable....

mean the common descent of all life on earth from a single ancestor via undirected mutation and natural selection -- that's a textbook definition of neo-Darwinism...

Lieutenant Pyotr Schmidt, was directed against the government, while some was undirected. It included terrorism, worker strikes, peasant unrest and military mutinies...

or density satisfies one of the Markov properties with respect to an undirected graph G if and only if it is a Gibbs random field, that is, its density...

triangulations, we observe that the weak dual graph to the triangulation (the undirected graph having one vertex per triangle and one edge per pair of adjacent...

Instead, they seek a coloring of the directed graph formed by doubling each undirected edge of the network, with the property that each directed edge uv has...

does not require a designer: "it is perhaps possible that evolution (undirected by God or anyone else) has somehow furnished us with our design plans"...

and vertices are junctions between them. The arcs may be directed or undirected due to the possible presence of one way streets or different costs in...

and of living things are best explained by an intelligent cause, not an undirected process such as natural selection." Its chief activities are a campaign...

spherical or nearly spherical nanoparticles, and in the form of oriented or undirected fibers. Properties, of the final material, defined as the set of properties...

In graph theory, a Trémaux tree of an undirected graph G {\displaystyle G} is a type of spanning tree, generalizing depth-first search trees. They are...

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

2^{m}} possible parent combinations. Similar ideas may be applied to undirected, and possibly cyclic, graphs such as Markov networks. Suppose we want...

hard to characterize, in strong contrast with the situation for signed undirected graphs. Signed digraphs should not be confused with oriented signed graphs...

conjecture involves embeddings of the shortest path distances of weighted undirected graphs into ℓ₁ spaces, real vector spaces in which the distance between...

number of different colours being used by its neighbors. Given a simple, undirected graph G {\displaystyle G} compromising a vertex set V {\displaystyle V}...

does not require a designer: "it is perhaps possible that evolution (undirected by God or anyone else) has somehow furnished us with our design plans"...

maximum-cardinality exchange, given the original directed graph G, construct an undirected bipartite graph H(X+Y, E) in which: Each pair j in G has two nodes: xj...

science, a graph is an abstract data type that is meant to implement the undirected graph and directed graph concepts from mathematics; specifically, the...

minimal spanning tree {ab, bc}. algorithm Borůvka is input: A weighted undirected graph G = (V, E). output: F, a minimum spanning forest of G. Initialize...

combinatorics is that the doubly-triangular numbers count the number of two-edge undirected multigraphs on n {\displaystyle n} labeled vertices. In this setting,...

sent from the source to the sink in the given network. In a weighted, undirected network, it is possible to calculate the cut that separates a particular...

_{y}d(y,x)} . Taking distances from or to all other nodes is irrelevant in undirected graphs, whereas it can produce totally different results in directed graphs...

are classified separately from forward edges. If the original graph is undirected then all of its edges are tree edges or back edges. It is also possible...

In combinatorial mathematics, an Apollonian network is an undirected graph formed by a process of recursively subdividing a triangle into three smaller...

It integrates into Excel 2010, 2013, 2016, 2019, 2021, 365 and adds undirected and directed graphs as a chart type to the spreadsheet and calculates...

In graph theory, the Hadwiger number of an undirected graph G is the size of the largest complete graph that can be obtained by contracting edges of G...

graphs are defined for digraphs, they may be extended to undirected graphs by replacing each undirected edge by a pair of oppositely ordered directed edges...

algorithms, such as the widely employed convolutional networks. Given an undirected weighted graph G = ( V , E ) {\displaystyle G=(V,E)} , where V {\displaystyle...

matroids defined from certain other types of mathematical object such as undirected graphs, matrices, and field extensions are important within the study...

Conway's 99-graph problem – a problem invented by Conway asking if a certain undirected graph exists Conway sequence – a self-referential sequence in which each...

the universal homogenous poset, all first-order reducts of homogenous undirected graphs, all first-order reducts of all unary structures, all CSPs in the...

Gavankar Papi is a lesbian and according to Alice Pieszecki's "chart" (an undirected labeled graph in which nodes represent individuals and lines represent...

doi:10.1137/S0097539795288246. S2CID 5221089. Thorup, Mikkel (1999). "Undirected single-source shortest paths with positive integer weights in linear time"...

these generalized notions of cliques can also be found by constructing an undirected graph whose edges represent related pairs of actors from the social network...

in the following form. According to it, if all proper colorings of an undirected graph G {\displaystyle G} use k {\displaystyle k} or more colors, then...

was Earthlings, a rarely used slang term for lesbians. "The Chart", an undirected labeled graph in which nodes represent individuals and lines represent...

n_{ij}=n_{ji},} we denote the two opposite arrows between χ i, χ j as an undirected edge of weight nij. Moreover, if n i j = 1 , {\displaystyle n_{ij}=1,}...

N ≫ 1 {\displaystyle N\gg K\gg \ln N\gg 1} , the model constructs an undirected graph with N {\displaystyle N} nodes and N K 2 {\displaystyle {\frac {NK}{2}}}...

an open problem in a paper from 1977. More precisely, for an arbitrary undirected graph H {\displaystyle H} , let F H {\displaystyle {\mathcal {F}}_{H}}...

theory), an assignment of a direction (orientation) to each edge of an undirected graph Orientation (mental), a function of the mind Romantic orientation...

Undirected graph named after S. S. Shrikhande...

Birkhoff. Nested dissection consists of the following steps: Form an undirected graph in which the vertices represent rows and columns of the system of...

(bilipschitz constant) is only logarithmic in the number of points. For any undirected connected graph G, the set V of vertices of G can be turned into a metric...

three edges per vertex has a Hamiltonian cycle. A planar graph is an undirected graph that can be embedded into the Euclidean plane without any crossings...

in hypergraphs. Formally, a vertex cover V ′ {\displaystyle V'} of an undirected graph G = ( V , E ) {\displaystyle G=(V,E)} is a subset of V {\displaystyle...

of problems whose solution is guaranteed by the handshaking lemma: any undirected graph with an odd degree vertex must have another odd degree vertex. It...

whether it is undirected or directed, which basically makes the distinction of whether there is a precise destination or not: undirected wayfinding means...

graph (RGG) is the mathematically simplest spatial network, namely an undirected graph constructed by randomly placing N nodes in some metric space (according...

is "no accident", as the protagonist stood in for the young Grogan's "undirected self". Grogan was also the author of Final Score, a crime novel published...

sub-network's hidden layer serves as the visible layer for the next. An RBM is an undirected, generative energy-based model with a "visible" input layer and a hidden...

either one or three neighbors. A free tree or unrooted tree is a connected undirected graph with no cycles. The vertices with one neighbor are the leaves of...

Classification, regression 2017 M. Li et al. KEGG Metabolic Reaction Network (Undirected) Dataset Network of metabolic pathways. A reaction network and a relation...

constraints on constructs those languages allow. In mathematics, a tree is an undirected graph in which any two vertices are connected by exactly one simple path...