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Graph formed by adding isolated or universal vertices
In graph theory, a threshold graph is a graph that can be constructed from a one-vertex graph by repeated applications of the following two operations:
Threshold_graph
Maximal subgraph whose vertices can reach each other
a percolation threshold, an edge probability above which a giant component exists and below which it does not. The components of a graph can be constructed
Component_(graph_theory)
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
Graph where every connected induced subgraph has a universal vertex
a graph is perfect." Trivially perfect graphs are also known as comparability graphs of trees, arborescent comparability graphs, and quasi-threshold graphs
Trivially_perfect_graph
Describing a family of graphs by excluding certain (sub)graphs
In graph theory, a branch of mathematics, many important families of graphs can be described by a finite set of individual graphs that do not belong to
Forbidden graph characterization
Forbidden_graph_characterization
Graph formed by complementation and disjoint union
more general graph classes. Special types of cograph include complete graphs, complete bipartite graphs, cluster graphs, and threshold graphs. Cographs are
Cograph
Threshold of percolation theory models
models of random systems or networks (graphs), and the nature of the connectivity in them. The percolation threshold is the critical value of the occupation
Percolation_threshold
Split graph String graph Strongly regular graph Threshold graph Total graph Tree (graph theory). Trellis (graph) Turán graph Ultrahomogeneous graph Vertex-transitive
List_of_graph_theory_topics
Topics referred to by the same term
cryptosystem Threshold displacement energy Threshold energy Threshold graph Threshold knowledge Threshold model Threshold voltage Thresholding (image processing)
Threshold
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
Recursively-formed graph with two terminal vertices
tree. Threshold graph Cograph Hanner polytope Series-parallel partial order Eppstein, David (1992). "Parallel recognition of series–parallel graphs" (PDF)
Series–parallel_graph
Graph defined from a set of points in the Euclidean plane
connectivity: if a random subset of fewer vertices than the threshold is given, the remaining graph will almost surely have only finite connected components
Gabriel_graph
Graph which partitions into a clique and independent set
In graph theory, a branch of mathematics, a split graph is a graph in which the vertices can be partitioned into a clique and an independent set. Split
Split_graph
Graph with same nodes as but complementary connections to another
gives an independent set and a clique in the complement graph. The threshold graphs are the graphs formed by repeatedly adding either an independent vertex
Complement_graph
Two closely related models for generating random graphs
the mathematical field of graph theory, the Erdős–Rényi models are two closely related models for generating random graphs and the evolution of a random
Erdős–Rényi_model
Graph with almost the max amount of edges
instead of single graph instances. They defined somewhere dense graph classes as those classes of graphs for which there exists a threshold t such that every
Dense_graph
Graph linking pairs of comparable elements in a partial order
Comparability graphs have also been called transitively orientable graphs, partially orderable graphs, containment graphs, and divisor graphs. An incomparability
Comparability_graph
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
dot product threshold, and the smallest possible value of k is called the dot product dimension. A threshold graph is a dot product graph with positive
Dot product representation of a graph
Dot_product_representation_of_a_graph
Evolutionary theory explaining polygyny
1 (monogamous line) and curve 2 (bigamous line) of the polygyny threshold model graph (see above) to be the cost of polygyny. N. B. Davies further defined
Polygyny_threshold_model
Mathematical proposition
known as the expectation threshold conjecture or more recently the Park-Pham Theorem, was a conjecture in the field of graph theory and statistical mechanics
Kahn–Kalai_conjecture
Graph with tight clique-coloring relation
In graph theory, a perfect graph is a graph in which the chromatic number equals the size of the maximum clique, both in the graph itself and in every
Perfect_graph
Computational problem of graph theory
In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights
Shortest_path_problem
Algorithm in graph theory
between graphs Transitive closure in AND/OR/threshold graphs. Implementations are available for many programming languages. For C++, in the boost::graph library
Floyd–Warshall_algorithm
Mathematical theory on behavior of connected clusters in a random graph
Study of graphs as a representation of relations between discrete objects Network science – Academic field Percolation threshold – Threshold of percolation
Percolation_theory
Graph measuring gene relationships
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
Gene_co-expression_network
Class of mating system in non-human species
breeding female. However, if the bigamous threshold is higher than the second female's original resource threshold, the female will enter into a polygynous
Polygyny_in_animals
Intersection graph of unit disks in the plane
below a fixed threshold. Unit disk graphs are the intersection graphs of equal-radius circles, or of equal-radius disks. These graphs have a vertex for
Unit_disk_graph
Theorem in graph theory
The Gale–Ryser theorem is a result in graph theory and combinatorial matrix theory, two branches of combinatorics. It provides one of two known approaches
Gale–Ryser_theorem
Vertex adjacent to all others in a graph
In graph theory, a universal vertex is a vertex of an undirected graph that is adjacent to all other vertices of the graph. It may also be called a dominating
Universal_vertex
Visible difference in brightness or color
expressed as the reciprocal of the threshold contrast for detection of a given pattern (i.e., 1 ÷ contrast threshold). Using the results of a contrast
Contrast_(vision)
Clustering and community detection algorithm
well-connected. Consider, for example, the following graph: Three communities are present in this graph (each color represents a community). Additionally
Leiden_algorithm
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)
Graph coloring with equal color classes
threshold of this graph is 2n + 2, significantly greater than its equitable chromatic number of two. Brooks' theorem states that any connected graph with
Equitable_coloring
When perception of one sound is affected by another sound
the first graph the masker is presented at a frequency of 250 Hz at the same time as the signal. The amount the masker increases the threshold of the signal
Auditory_masking
Graph generated by a random process
In mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability
Random_graph
Diagnostic plot of binary classifier ability
left corner in a DET plot. Furthermore, DET graphs have the useful property of linearity and a linear threshold behavior for normal distributions. The DET
Receiver operating characteristic
Receiver_operating_characteristic
graph, chordal bipartite graph, or chain graph. It can be solved in polynomial time for split graphs, threshold graphs, and graphs in which every five vertices
Graph_sandwich_problem
Problem on triangles in graph theory
also known to hold for graphs of treewidth at most six, for threshold graphs, for sufficiently dense graphs, and for chordal graphs that contain a large
Tuza's_conjecture
Point where the curvature of a curve changes sign
at which the curvature changes sign. In particular, in the case of the graph of a function, it is a point where the function changes from being concave
Inflection_point
Concept in network science
exhibit a sharp threshold effect reminiscent of percolation thresholds. Suppose that we allow the size n {\displaystyle n} of the graph to grow, keeping
Stochastic_block_model
Sports medicine test
test intended to measure an individual's maximum anaerobic and aerobic threshold heart rates. The test measures a person's heart rate at different loads
Conconi_test
In the mathematical field of graph theory, a word-representable graph is a graph that can be characterized by a word (or sequence) whose entries alternate
Word-representable_graph
Graph operation
construct any critical graph or any graph whose chromatic number is at least some given threshold. Let G and H be two undirected graphs, vw be an edge of G
Hajós_construction
In graph theory, toughness is a measure of the connectivity of a graph. A graph G is said to be t-tough for a given real number t if, for every integer
Graph_toughness
Rate of increase of a laser's output power with increasing input power
way the threshold pump power for this particular laser can be found. Determining the laser threshold periodically, via a slope efficiency graph, is particularly
Slope_efficiency
Statistical measure of a binary classification
sensitivity and specificity. The black, dotted line in the center of the graph is where the sensitivity and specificity are the same. As one moves to the
Sensitivity_and_specificity
How brains and associative networks search for information
Firing threshold F, a real number in the range [0.0 ... 1.0] Decay factor D, a real number in the range [0.0 ... 1.0] Steps: Initialize the graph setting
Spreading_activation
certain threshold distance, or a decaying function of hyperbolic distance yielding the connection probability). A HGG generalizes a random geometric graph (RGG)
Hyperbolic_geometric_graph
Description of degree sequences of graphs
theorem is a result in graph theory, a branch of combinatorial mathematics. It provides one of two known approaches to solving the graph realization problem
Erdős–Gallai_theorem
Intersection graph of unit intervals on the real line
In graph theory, a branch of mathematics, an indifference graph is an undirected graph constructed by assigning a real number to each vertex and connecting
Indifference_graph
Competitive balance tax in Major League Baseball
consecutive seasons above the CBT threshold, but this was not always the case. If a club "dips below the luxury tax threshold for a season, the penalty level
Major League Baseball luxury tax
Major_League_Baseball_luxury_tax
In graph theory, the mathematically simplest spatial network
In graph theory, a random geometric graph (RGG) is the mathematically simplest spatial network, namely an undirected graph constructed by randomly placing
Random_geometric_graph
Measurement of graph sparsity
In graph theory, a k-degenerate graph is an undirected graph in which every subgraph has at least one vertex of degree at most k {\displaystyle k} . That
Degeneracy_(graph_theory)
Electrical signal inhibiting a neuron from firing
membrane must depolarize—the membrane potential must reach a voltage threshold more positive than the resting membrane potential. Therefore, hyperpolarisation
Inhibitory postsynaptic potential
Inhibitory_postsynaptic_potential
Minimum sound level that an average human can hear
The absolute threshold of hearing (ATH), also known as the absolute hearing threshold or auditory threshold, is the minimum sound level of a pure tone
Absolute_threshold_of_hearing
Third subphase of interphase
cyclin B1. These experiments show that the threshold concentration for entering M-phase is higher than the threshold for exiting M-phase: nuclear envelope
G2_phase
Mathematical game played on a graph
Graph pebbling is a mathematical game played on a graph with zero or more pebbles on each of its vertices. 'Game play' is composed of a series of pebbling
Graph_pebbling
Type of sub-graph
frequency FG of G′ in G. A graph is called recurrent (or frequent) in G when its frequency FG(G′) is above a predefined threshold or cut-off value. We use
Network_motif
Large connected component of a random graph
probability that the whole random graph is connected. A similar sharp threshold between parameters that lead to graphs with all components small and parameters
Giant_component
following graph depicts the evolution of standings of the main political parties in the polling average since last parliamentary election. The graph shows
Opinion polling for the next Slovenian parliamentary election
Opinion_polling_for_the_next_Slovenian_parliamentary_election
Heuristic pathfinding algorithm
Iterative deepening A* (IDA*) is a graph traversal and path search algorithm that can find the shortest path between a designated start node and any member
Iterative_deepening_A*
Structure-preserving correspondence between node-link graphs
In the mathematical field of graph theory, a graph homomorphism is a mapping between two graphs that respects their structure. More concretely, it is a
Graph_homomorphism
vertices when the similarity value between them is above some threshold. In the similarity graph, the more edges exist for a given number of vertices, the
HCS_clustering_algorithm
Louis Lapicque suggested that the action potential was generated as a threshold was crossed, what would be later shown as a product of the dynamical systems
History_of_neuroscience
Binary operation in graph theory
In graph theory, the strong product is a way of combining two graphs to make a larger graph. Two vertices are adjacent in the strong product when they
Strong_product_of_graphs
Type of mathematical function
breakpoints, changepoints, threshold values or knots. As in many applications, this function is also continuous. The graph of a continuous piecewise linear
Piecewise_linear_function
alternative exists in the form of graph-based segmentation methods. The connectivity information inherent to graphs allows performing independent work
Minimum spanning tree-based segmentation
Minimum_spanning_tree-based_segmentation
Dimensionality reduction of graph-based semantic data objects [machine learning task]
In representation learning, knowledge graph embedding (KGE), also called knowledge representation learning (KRL), or multi-relation learning, is a machine
Knowledge_graph_embedding
Process for achieving system stability
themselves. The smallest threshold that allows some cells of an initial cluster to survive is called the degeneracy of its adjacency graph, and the remnant of
Bootstrap_percolation
Country in northwestern Europe
archived from the original on 5 July 2019, retrieved 10 December 2019 Tables, Graphs and Maps Interface (TGM) table. Eurostat (26 February 2013). Retrieved 12
United_Kingdom
Clustering methods
similarity graph is constructed using a hard connectivity criterion (i.e., binary adjacency based on whether two nodes are within a threshold distance)
Spectral_clustering
Threshold host density (NT), in the context of wildlife disease ecology, refers to the concentration of a population of a particular organism as it relates
Threshold_host_density
Type of brain cell
concentration. The latter supports the existence of a threshold. The graphs which show these characteristics are referred to as Michaelis-Menten graphs
Astrocyte
On short connecting nets with added points
than some given threshold, is NP-complete, which implies that the optimization variant, asking for the minimum-weight tree in a given graph, is NP-hard.
Steiner_tree_problem
2001 book by Joel Spencer
The Strange Logic of Random Graphs is a book on zero-one laws for random graphs. It was written by Joel Spencer and published in 2001 by Springer-Verlag
The Strange Logic of Random Graphs
The_Strange_Logic_of_Random_Graphs
Type of probability threshold analysis
the threshold probability yields an estimate of net benefit that incorporates decision consequences and preferences. A decision curve analysis graph is
Decision_curve_analysis
Tisza Party won a two-thirds supermajority, which is the legislative threshold to amend the Fundamental Law of Hungary. In the process, it won both the
2026 Hungarian parliamentary election
2026_Hungarian_parliamentary_election
In computational geometry and geometric graph theory, a β-skeleton or beta skeleton is an undirected graph defined from a set of points in the Euclidean
Beta_skeleton
List of Windows 10 operating system versions
version of Windows 10 (also retroactively named version 1507 and codenamed "Threshold 1") was released in July 2015. It carries the build number 10.0.10240;
Windows_10_version_history
remaining graph is not empty: 3. Add a vertex u to S, where u has minimum degree in the remaining graph. 4. Delete u and all of its neighbors from the graph. 5
Method of conditional probabilities
Method_of_conditional_probabilities
Logical formulation of graph properties
the mathematical fields of graph theory and finite model theory, the logic of graphs deals with formal specifications of graph properties using sentences
Logic_of_graphs
Input power level at which a laser generates light primarily by stimulated emission
In laser science, the lasing threshold is the lowest excitation level at which a laser's output is dominated by stimulated emission rather than by spontaneous
Lasing_threshold
Mathematician at Courant Institute of Mathematical Sciences
Mathematical Sciences at New York University working in combinatorics and graph theory. She and Huy Tuan Pham proved the Kahn–Kalai conjecture on estimating
Jinyoung_Park_(mathematician)
Digital circuit without clock cycles
Power Multi-threshold Asychronous Circuit Design". Retrieved 2011-12-12. Rosenblum, L. Ya.; Yakovlev, A. V. (July 1985). "Signal Graphs: from Self-timed
Asynchronous_circuit
Free open source RRDtool
RRDtool. Cacti allows a user to poll services at predetermined intervals and graph the resulting data. Through the use of Cacti plugins, it has been extended
Cacti_(software)
Data visualization
points. Each of the n {\displaystyle n} samples is then represented on the graph by assigning the mean of the two measurements as the x {\displaystyle x}
Bland–Altman_plot
Complexity class of problems
problems that are considered good candidates for being NP-intermediate are the graph isomorphism problem, and decision versions of factoring and the discrete
NP-intermediate
Properties of mathematical relationships
than two. The use of the term for polynomials stems from the fact that the graph of a polynomial in one variable is a straight line. In the term "linear
Linearity
Mass extinction event c. 444 million years ago
The blue graph shows the apparent percentage (not the absolute number) of marine animal genera becoming extinct during any given time interval. It does
Late Ordovician mass extinction
Late_Ordovician_mass_extinction
Measure of ionization of air by ionizing radiation
To see the model, please see dashed line in the graph "Dose response curve of linear-non-threshold model". Because of this uncertainty at low doses,
Radiation_exposure
Runoff election process
when three candidates from the first round have reached the retention threshold, and none of them withdraws from the second round. The winner of this
Triangular_election_in_France
Intelligence of machines
21), Domingos (2015, Chapter 4) Gradient calculation in computational graphs, backpropagation, automatic differentiation: Russell & Norvig (2021, sect
Artificial_intelligence
Minimum spanning forest algorithm that greedily adds edges
algorithm finds a minimum spanning forest of an undirected edge-weighted graph. If the graph is connected, it finds a minimum spanning tree. It is a greedy algorithm
Kruskal's_algorithm
Network with non-trivial topological features
network is a graph (network) with non-trivial topological features—features that do not occur in simple networks such as lattices or random graphs but often
Complex_network
Digital image analysis tool
vision, image histograms can be useful tools for thresholding. Because the information contained in the graph is a representation of pixel distribution as
Image_histogram
Subset of artificial intelligence
difference between clusters. Other methods are based on estimated density and graph connectivity. A special type of unsupervised learning called self-supervised
Machine_learning
Minimum audibility curve is a standardized graph of the threshold of hearing frequency for an average human, and is used as the reference level when measuring
Minimum_audibility_curve
Interaction, No Setup, and Perfect Soundness" 2024 Brice Huang (MIT) "Capacity Threshold for the Ising Perceptron" 2023 Rahul Ilango (MIT) "SAT Reduces to the
Machtey_Award
Partition of a graph's nodes into cliques
In graph theory, a clique cover or partition into cliques of a given undirected graph is a collection of cliques that cover the whole graph. Generally
Clique_cover
THRESHOLD GRAPH
THRESHOLD GRAPH
Surname or Lastname
German (also Gräff), Dutch, and Jewish (Ashkenazic)
German (also Gräff), Dutch, and Jewish (Ashkenazic) : variant of Graf.English : metonymic occupational name for a clerk or scribe, from Anglo-Norman French grafe ‘quill’, ‘pen’ (a derivative of grafer ‘to write’, Late Latin grafare, from Greek graphein).
Boy/Male
Arabic, Muslim
Gateway; Threshold
Girl/Female
Latin
Goddess of the threshold.
Boy/Male
Italian Spanish
Enduring. The poet Dante Alighieri wrote The Divine Comedy with its graphic description of...
Biblical
threshold; silver cup
Boy/Male
Muslim/Islamic
Threshold
Boy/Male
Indian
Threshold
Girl/Female
Australian, French, Indian, Latin, Malayalam
Cultural; Goddess of the Threshold
Surname or Lastname
English
English : probably a variant spelling of Purcell, or alternatively of Percil (from Old French percer ‘to pierce’ + soel, suel ‘threshold’).
Surname or Lastname
English
English : occupational name for someone who did piece-work (especially someone who threshed grain), from an agent derivative of Anglo-Norman French tasque ‘task’ (Old French tasche, Late Latin taxa, of uncertain origin).Slovenian (Tašker) : unexplained.
Boy/Male
Italian Spanish
Enduring. The poet Dante Alighieri wrote The Divine Comedy with its graphic description of...
Boy/Male
Biblical
Threshold, silver cup.
Boy/Male
Spanish American Italian Latin
Enduring. The poet Dante Alighieri wrote The Divine Comedy with its graphic description of...
Boy/Male
Arabic, Muslim
Threshold; Gateway
Boy/Male
Italian Spanish
Enduring. The poet Dante Alighieri wrote The Divine Comedy with its graphic description of...
Boy/Male
Arabic, French, Gujarati, Hindu, Indian, Muslim, Sindhi
Old Arabic Name; Threshold
Boy/Male
Muslim
Threshold
Surname or Lastname
English
English : variant of Selman.German (Sillmann) : possibly a variant of Sieler, or a topographic name for someone living on a ridge, from Low German süll, sill ‘sill’, ‘threshold’, ‘ramp’.
Girl/Female
Latin
Goddess of the threshold.
THRESHOLD GRAPH
THRESHOLD GRAPH
Girl/Female
Celtic
Strong.
Girl/Female
Hindu, Indian
Best
Boy/Male
Hindu
Boy/Male
Greek
Earth.
Boy/Male
Indian
Thirsty
Girl/Female
Arabic, Australian, Muslim
Fortune; Wealth; Riches
Girl/Female
Hindu
Girl/Female
Arabic, Muslim
Cute Flower
Girl/Female
Arabic, Australian, French, German
The Weaning; The Abstaining
Girl/Female
Assamese, Indian
Rounded
THRESHOLD GRAPH
THRESHOLD GRAPH
THRESHOLD GRAPH
THRESHOLD GRAPH
THRESHOLD GRAPH
a.
Consisting of three, or thrice repeated; triple; as, threefold justice.
a.
Threefold; triple.
n.
The stone forming a threshold.
a.
Threefold.
n.
The sill or threshold of a door.
a.
Triple; treble; threefold.
n.
Threshold.
a.
Threefold; triple; consisting of three; ternate.
n.
Fig.: The place or point of entering or beginning, entrance; outset; as, the threshold of life.
v. t.
To step over; to stride over or across; as, to bestride a threshold.
a.
Threefold; thrice-paired.
v. t.
Made thrice as much; threefold; tripled.
n.
The timber or stone at the foot of a door; the threshold.
n.
Threshold.
v. i.
To become threefold.
adv.
In a threefold manner or degree; repeatedly; very.
v. t.
To make thrice as much; to make threefold.
imp. & p. p.
of Thresh
a.
The quality or state of being triple, or threefold; trebleness.
n.
The plank, stone, or piece of timber, which lies under a door, especially of a dwelling house, church, temple, or the like; the doorsill; hence, entrance; gate; door.