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Function graph representing factorization
A factor graph is a bipartite graph representing the factorization of a function. In probability theory and its applications, factor graphs are used to
Factor_graph
Partition of a graph into spanning subgraphs
is 1-factorable. If n is even and k ≥ n − 1 then G is 1-factorable. More unsolved problems in mathematics In graph theory, a factor of a graph G is a
Graph_factorization
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
Algorithm for statistical inference on graphical models
operates on a factor graph. A factor graph is a bipartite graph containing nodes corresponding to variables V {\displaystyle V} and factors F {\displaystyle
Belief_propagation
Correction factor which describes the deviation of a real gas from ideal gas behavior
generalized compressibility factor graphs based on as many as 25 or more different pure gases, such as the Nelson-Obert graphs. Such graphs are said to have an
Compressibility_factor
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
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
constraint satisfaction problem. A constraint graph is a special case of a factor graph, which allows for the existence of free variables. The constraint hypergraph
Constraint_graph
Rating system supporting games with more than 2 players
(wins and draws) introduce non-Gaussian terms. In the factor graph, these appear as comparison factors that impose inequalities on performance differences
TrueSkill
Topics referred to by the same term
algebra A von Neumann algebra, with a trivial center Factor (graph theory), a spanning sub graph Any finite contiguous sub-sequence of a word in combinatorics
Factor
Graph of triangles with a shared vertex
the mathematical field of graph theory, the friendship graph (or Dutch windmill graph or n-fan) Fn is a planar, undirected graph with 2n + 1 vertices and
Friendship_graph
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
Topics referred to by the same term
in an hour K-factor (actuarial), the ratio of the value of deferrable expenses to the value of estimated gross profits k-factor (graph theory), a spanning
K-factor
Methodic assignment of colors to elements of a graph
In graph theory, graph coloring is a methodic assignment of labels traditionally called "colors" to elements of a graph. The assignment is subject to certain
Graph_coloring
Cubic graph with 10 vertices and 15 edges
bridgeless graph has a cycle-continuous mapping to the Petersen graph. More unsolved problems in mathematics In the mathematical field of graph theory, the
Petersen_graph
Area of discrete mathematics
computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context
Graph_theory
Mathematical parameter of embeddings
or dilation of the mapping. The stretch factor is important in the theory of geometric spanners, weighted graphs that approximate the Euclidean distances
Stretch_factor
Set of edges without common vertices
In the mathematical discipline of graph theory, a matching or independent edge set in an undirected graph is a set of edges without common vertices. In
Matching_(graph_theory)
Class of artificial neural networks
Graph neural networks (GNNs) are artificial neural networks designed for tasks whose inputs are graphs. Because graphs usually do not have a canonical
Graph_neural_network
Canadian computer scientist (born 1968)
propagation algorithm for clustering and data summarization, and the factor graph notation for probability models. In the late 1990s, Frey was a leading
Brendan_Frey
Concept in mathematics
length 1), is a connected graph of infinite diameter. For every integer n ≥ 2 {\displaystyle n\geq 2} , the free factor graph F n ( 1 ) {\displaystyle
Free_factor_complex
Decomposition of a graph into hamiltonion cycles
of the graph such that each factor is connected. For a Hamiltonian decomposition to exist in an undirected graph, the graph must be connected and regular
Hamiltonian_decomposition
Concept in graph theory
In graph theory, a strongly regular graph (SRG) is a regular graph G = (V, E) with v vertices and degree k such that for some given integers λ , μ ≥ 0
Strongly_regular_graph
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
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
Measure of relative importance of a journal
The impact factor (IF) or journal impact factor (JIF) of an academic journal is a type of journal ranking. Journals with higher impact-factor values are
Impact_factor
Regular graph with fewest possible nodes for its girth
of graph theory, a cage is a regular graph that has as few vertices as possible for its girth. Formally, an (r, g)-graph is defined to be a graph in which
Cage_(graph_theory)
Measurement of graph sparsity
how sparse it is, and is within a constant factor of other sparsity measures such as the arboricity of a graph. Degeneracy is also known as the k-core number
Degeneracy_(graph_theory)
Linear error correcting code
Below is a graph fragment of an example LDPC code using Forney's factor graph notation. In this graph, n variable nodes in the top of the graph are connected
Low-density_parity-check_code
Graph that misrepresents data
In statistics, a misleading graph, also known as a distorted graph, is a graph that misrepresents data, constituting a misuse of statistics and with the
Misleading_graph
Graph of numbers differing by a square
Paley graphs form an infinite family of conference graphs, which yield an infinite family of symmetric conference matrices. Paley graphs allow graph-theoretic
Paley_graph
Binary operation in graph theory
pairs of vertices in the factor graphs that are either adjacent or identical. The strong product is one of several different graph product operations that
Strong_product_of_graphs
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
Theorem in graph theory
mathematical discipline of graph theory, the 2-factor theorem, discovered by Julius Petersen, is one of the earliest works in graph theory. It can be stated
2-factor_theorem
decomposition of a complete graph of even order minus a 1-factor (a perfect matching) into even cycles and a complete graph of odd order into odd cycles
Cycle decomposition (graph theory)
Cycle_decomposition_(graph_theory)
Method for accident analysis to determine causal relationships
is a directed acyclic graph, the nodes of which are factors. Directed edges denote cause–effect relations between the factors. Why–because analyses start
Why–because_analysis
Type of graph related to pursuit–evasion
In graph theory, a cop-win graph is an undirected graph on which the pursuer (cop) can always win a pursuit–evasion game against a robber, with the players
Cop-win_graph
Subdivision of vertices into disjoint sets
However, uniform graph partitioning or a balanced graph partition problem can be shown to be NP-complete to approximate within any finite factor. Even for special
Graph_partition
Computational navigational technique used by robots and autonomous vehicles
EKF fails. In robotics, GraphSLAM is a SLAM algorithm which uses sparse information matrices produced by generating a factor graph of observation interdependencies
Simultaneous localization and mapping
Simultaneous_localization_and_mapping
Geometric graph with unit edge lengths
In mathematics, particularly geometric graph theory, a unit distance graph is a graph formed from a collection of points in the Euclidean plane by connecting
Unit_distance_graph
Graph where every edge is in one triangle
In graph theory, a locally linear graph is an undirected graph in which every edge belongs to exactly one triangle. Equivalently, for each vertex of the
Locally_linear_graph
Operation in graph theory
In graph theory, the Cartesian product G □ H of graphs G and H is a graph such that: the vertex set of G □ H is the Cartesian product V(G) × V(H); and
Cartesian_product_of_graphs
Algorithm for finding shortest paths
an algorithm for finding the shortest paths between nodes in a weighted graph, which may represent, for example, a road network. It was conceived by computer
Dijkstra's_algorithm
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
Graph used in fluid dynamics
diagram (also Stanton diagram) is a graph in non-dimensional form that relates the Darcy–Weisbach friction factor fD, Reynolds number Re, and surface
Moody_chart
Partition of graph into sequence of paths
of edges. A factor-critical graph is a graph with an odd number of vertices, such that for each vertex v, if v is removed from the graph then the remaining
Ear_decomposition
Probabilistic model
Bayesian network learning (TBNL) A factor graph is an undirected bipartite graph connecting variables and factors. Each factor represents a function over the
Graphical_model
exploiting the power of factor graphs. Introduction Digital communication Estimation theory and Monte Carlo techniques Factor graphs and the Sum-Product algorithm
Iterative_Receiver_Design
3-regular graph with no 3-edge-coloring
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
Snark_(graph_theory)
Undirected graph acted on by a vertex-transitive cyclic group of symmetries
In graph theory, a circulant graph is an undirected graph acted on by a cyclic group of symmetries which takes any vertex to any other vertex. It is sometimes
Circulant_graph
Set of random variables
theorem) the graph is chordal (by equivalence to a Bayesian network) When such a factorization does exist, it is possible to construct a factor graph for the
Markov_random_field
Algorithm to search the nodes of a graph
tree or graph data structures. The algorithm starts at the root node (selecting some arbitrary node as the root node in the case of a graph) and explores
Depth-first_search
One of two different regular graphs with 16 vertices
field of graph theory, the Clebsch graph is either of two complementary graphs on 16 vertices, a 5-regular graph with 40 edges and a 10-regular graph with
Clebsch_graph
Academic journal
the journal has a 2020 impact factor of 0.857. Frank Harary, a biographical sketch at the ACM SIGACT site "Journal of Graph Theory". 2020 Journal Citation
Journal_of_Graph_Theory
Type of geometric spanner graph
computational geometry, the Theta graph, or Θ {\displaystyle \Theta } -graph, is a type of geometric spanner similar to a Yao graph. The basic method of construction
Theta_graph
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
Graph path which is an induced subgraph
In the mathematical area of graph theory, an induced path in an undirected graph G is a path that is an induced subgraph of G. That is, it is a sequence
Induced_path
Type of chart
A bar chart or bar graph is a chart or graph that presents categorical data with rectangular bars with heights or lengths proportional to the values that
Bar_chart
Statistics concept
networks and has a power of expression equivalent to probabilistic factor graphs. A Bayesian program is a means of specifying a family of probability
Bayesian_programming
Probabilistic graphical representation of causal relationships
of variables and their conditional dependencies via a directed acyclic graph (DAG). While it is one of several forms of causal notation, causal networks
Bayesian_network
British television series (2004–2018)
The X Factor is a British reality television music competition – that spawned the global X Factor franchise – created by Simon Cowell. Premiering on 4
The X Factor (British TV series)
The_X_Factor_(British_TV_series)
Operation in graph theory
In graph theory, the tensor product G × H of graphs G and H is a graph such that the vertex set of G × H is the Cartesian product V(G) × V(H); and vertices
Tensor_product_of_graphs
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
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 of short distances in another 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
Graph_power
Basque engineer, university teacher and politician
Henk. "Research Team". Retrieved 2023-12-28. Ochandiano, Pello (2012). Factor Graph Based Detection Schemes for Mobile Terrestrial DVB Systems with Long
Pello_Otxandiano
Unrelated vertices in graphs
In graph theory, an independent set, stable set, coclique or anticlique is a set of vertices in a graph, no two of which are adjacent. That is, it is a
Independent set (graph theory)
Independent_set_(graph_theory)
Matching which covers every node of the graph
In graph theory, a perfect matching in a graph is a matching that covers every vertex of the graph. More formally, given a graph G with edges E and vertices
Perfect_matching
Edges that hit all cycles in a graph
In graph theory and graph algorithms, a feedback arc set or feedback edge set in a directed graph is a subset of the edges of the graph that contains at
Feedback_arc_set
Family of graphs with 2n nodes and n(n-1) edges
In graph theory, a branch of mathematics, a crown graph on 2n vertices is an undirected graph with two sets of vertices {u1, u2, …, un} and {v1, v2, …
Crown_graph
Graph with a prism as its skeleton
mathematical field of graph theory, a prism graph is a graph that has one of the prisms as its skeleton. The individual graphs may be named after the
Prism_graph
Scheme for controlling errors in data over noisy communication channels
decoding algorithm works best when there are not short cycles in the factor graph that represents the decoder; the interleaver is chosen to avoid short
Error_correction_code
Pictorial representation of the behavior of subatomic particles
device of covariant perturbation theory, the graphs were called Feynman–Dyson diagrams or Dyson graphs, because the path integral was unfamiliar when
Feynman_diagram
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)
German-Canadian electrical engineer (born 1962)
late 1990s till early 2000s, Kschischang and Brendan Frey co-invented factor graph, a kind of graphical model used in Bayesian inference. Kschischang became
Frank_Kschischang
Maximum number of colors in a greedy graph coloring
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
Grundy_number
Intersection graph of unit disks in the plane
definitions of the unit disk graph, equivalent to each other up to a choice of scale factor: Unit disk graphs are the graphs formed from a collection of
Unit_disk_graph
Derived graph of higher chromatic number
In the mathematical area of graph theory, the Mycielskian or Mycielski graph of an undirected graph is a larger graph formed from it by a construction
Mycielskian
Resonator damping parameter
quality factor or Q factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is. Resonators with high quality factors have
Q_factor
Subset of a graph's vertices, including at least one endpoint of every edge
In graph theory, a vertex cover (sometimes node cover) of a graph is a set of vertices that includes at least one endpoint of every edge of the graph. In
Vertex_cover
Graph with all vertices of degree 4
mathematical field of graph theory, a quartic graph is a graph where all vertices have degree 4. In other words, a quartic graph is a 4-regular graph. Several well-known
Quartic_graph
Type of weighted geometric graph
the graph with weight at most t times the spatial distance between its endpoints. The parameter t is called the stretch factor or dilation factor of the
Geometric_spanner
Flow graph invented by Claude Shannon
A signal-flow graph or signal-flowgraph (SFG), invented by Claude Shannon, but often called a Mason graph after Samuel Jefferson Mason who coined the
Signal-flow_graph
Electronic calculator capable of plotting graphs
A graphing calculator (also graphics calculator or graphic display calculator) is a handheld computer that is capable of plotting graphs, solving simultaneous
Graphing_calculator
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
Probabilistic graphical model
inference methods for discrete graphical models; supports arbitrary factor graphs with discrete variables, including discrete Markov Random Fields and
Dynamic_Bayesian_network
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
Intersection graph representing regions on the Euclidean plane
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
Map_graph
Proposition on the domination number of Cartesian products of graphs
the other factor, dominating which requires at least γ(G)γ(H) vertices. Vizing's conjecture is also known to hold for cycles and for graphs with domination
Vizing's_conjecture
Longest distance between two vertices
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
Diameter_(graph_theory)
Graph where all long cycles have a chord
In the mathematical area of graph theory, a chordal graph is one in which all cycles of four or more vertices have a chord, which is an edge that is not
Chordal_graph
Graph with all vertices of degree 3
of graph theory, a cubic graph is a graph in which all vertices have degree three. In other words, a cubic graph is a 3-regular graph. Cubic graphs are
Cubic_graph
Graph without triples of adjacent vertices
area of graph theory, a triangle-free graph is an undirected graph in which no three vertices form a triangle of edges. Triangle-free graphs may be equivalently
Triangle-free_graph
Undirected graph
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
Critical_graph
Statement in mathematical combinatorics
its graph-theoretic forms, states that one will find monochromatic cliques in any edge labelling (with colours) of a sufficiently large complete graph. As
Ramsey's_theorem
Intersection graph of a chord diagram
In graph theory, a circle graph is the intersection graph of a chord diagram. That is, it is an undirected graph whose vertices can be associated with
Circle_graph
Undirected graph with 14 vertices
mathematical field of graph theory, the Heawood graph is an undirected graph with 14 vertices and 21 edges, named after Percy John Heawood. The graph is cubic, and
Heawood_graph
Measure of the structural complexity of a software program
Cyclomatic complexity is computed using the control-flow graph of the program. The nodes of the graph correspond to indivisible groups of commands of a program
Cyclomatic_complexity
Type of computer science algorithm
one wishes to know if two vertices in a graph of n vertices are in the same connected component of the graph, there is no known simple, deterministic
In-place_algorithm
Subset of a graph's nodes such that all other nodes link to at least one
In graph theory, a dominating set for a graph G is a subset D of its vertices, such that any vertex of G is in D, or has a neighbor in D. The domination
Dominating_set
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