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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
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
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
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
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
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)
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
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
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
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
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
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
Theorem in graph theory
the contrary sequences of threshold sequences with only one unique bigraphic realization, which is known as threshold graph. Minconvex sequences generalize
Gale–Ryser_theorem
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
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
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)
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 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
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
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
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
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
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
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
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
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
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
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
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
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
Study of Boolean functions via discrete Fourier analysis
so this is a coarse threshold. Friedgut's sharp threshold theorem states, roughly speaking, that a monotone graph property (a graph property is a property
Analysis_of_Boolean_functions
Partitioning a digital image into segments
method of image segmentation is called the thresholding method. This method is based on a clip-level (or a threshold value) to turn a gray-scale image into
Image_segmentation
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 don't contain a
Tuza's_conjecture
electoral threshold to win seats under the closed list, proportional representation electoral system. Ten parties succeeded in crossing the threshold. On 21
2022 Israeli legislative election
2022_Israeli_legislative_election
Concept in network science
models exhibit a sharp threshold effect reminiscent of percolation thresholds. Suppose that we allow the size n of the graph to grow, keeping the community
Stochastic_block_model
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 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
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
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
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
Sequence of locally optimal choices
distributed hash table. Graph theory is a rich source of greedy algorithms. Computing scientists frequently use greedy algorithms to compute graph invariants. Dijkstra's
Greedy_algorithm
Medical test
Pure-tone audiometry is the main hearing test used to identify hearing threshold levels of an individual, enabling determination of the degree, type and
Pure-tone_audiometry
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
Knesset seat counts rather than percentages, unless otherwise stated. This graph shows the polling trends from the 2022 Israeli legislative election until
Opinion polling for the 2026 Israeli legislative election
Opinion_polling_for_the_2026_Israeli_legislative_election
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
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
Single DNA sequences obtained from a high-throughput analysis of marker genes
sequences based on a threshold of similarity. Compared to ASVs, OTUs reflect a coarser notion of similarity. Though there is no single threshold, the most commonly
Amplicon_sequence_variant
They also include candidates from parties that passed the electoral threshold in 2022, and therefore have access to public campaign funding, free radio
Opinion polling for the 2026 Brazilian presidential election
Opinion_polling_for_the_2026_Brazilian_presidential_election
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
Measurement of graph sparsity
In graph theory, a k-degenerate graph is an undirected graph in which every non-empty subgraph has at least one vertex of degree at most k {\displaystyle
Degeneracy_(graph_theory)
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
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
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*
proportional representation in a single nationwide constituency. The electoral threshold for this election was 3.25%. Two parties could sign a surplus-vote agreement
2021 Israeli legislative election
2021_Israeli_legislative_election
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
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
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
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
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
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
Intelligence in machines
21), Domingos (2015, Chapter 4) Gradient calculation in computational graphs, backpropagation, automatic differentiation: Russell & Norvig (2021, sect
Artificial_intelligence
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
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
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
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
Measurement in electrophoresis methods
corresponding RFU values. An RFU peak is a relative maximum point along a graph of the analyzed data. The data can be normalized to DNA input or additional
Relative_fluorescence_units
Hungarian mathematician
József Balogh is a Hungarian-American mathematician, specializing in graph theory and combinatorics. Balogh grew up in Mórahalom and attended secondary
József_Balogh_(mathematician)
Mathematical game played on a graph
pebbling, domination cover pebbling, bounds, and thresholds for pebbling numbers, as well as deep graphs. One application of pebbling games is in the security
Graph_pebbling
the percentages, as though there were no threshold; others eliminated parties that polled below the threshold and distributed the 120 available Knesset
Opinion polling for the April 2019 Israeli legislative election
Opinion_polling_for_the_April_2019_Israeli_legislative_election
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)
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
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
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
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
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
Measure of organism response to stimulus
first point along the graph where a response above zero (or above the control response) is reached is usually referred to as a threshold dose. For most beneficial
Dose–response_relationship
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
Range of frequencies that can be heard by humans or other animals
A basic measure of hearing is afforded by an audiogram, a graph of the absolute threshold of hearing (minimum discernible sound level) at various frequencies
Hearing_range
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
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
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)
Visual representation of data
A horizon chart or horizon graph is a 2-dimensional data visualization displaying a quantitative data over a continuous interval, most commonly a time
Horizon_chart
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
colloquial and informal. While a threshold for a particular network may be invented, there is no universal threshold that defines what much fewer actually
Sparse_network
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
Cryptographic algorithm created by Adi Shamir
shares is needed, called the threshold. No information about the secret can be gained from any number of shares below the threshold (a property called perfect
Shamir's_secret_sharing
Network service attack performed by multiple fake identities
approaches to Sybil attack prevention include identity validation, social trust graph algorithms, economic costs, personhood validation, and application-specific
Sybil_attack
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
Probability saying
Vojtech; Rucinski, Andrzej; Tetali, Prasad (January 2006). "A Sharp Threshold for Random Graphs with a Monochromatic Triangle in Every Edge Coloring". Memoirs
Almost_surely
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
Knesset seat counts rather than percentages, unless otherwise stated. This graph shows the polling trends from the 2021 Israeli legislative election until
Opinion polling for the 2022 Israeli legislative election
Opinion_polling_for_the_2022_Israeli_legislative_election
differently during the DAT test, and are measured on a graph. The test determines the threshold, or minimum light intensity required to produce a visual
Dark_adaptation_threshold
Graphics structure
insertions and removals crossed the threshold, and other more refined heuristics). BVHs can also be combined with scene graph methods, and geometry instancing
Bounding_volume_hierarchy
Israeli Arab party voting lists
triple in the elections, whilst the UAL failed to cross the electoral threshold. Alongside the defeat of two other lists, the Christian-led Arab Brotherhood
Arab_satellite_lists
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
Monitoring system in computer drives
values: "threshold not exceeded" and "threshold exceeded". Often, these are represented as "drive OK" or "drive fail" respectively. A "threshold exceeded"
Self-Monitoring, Analysis and Reporting Technology
Self-Monitoring,_Analysis_and_Reporting_Technology
Database management system by SAP
spatial data processing, text analytics, text search, streaming analytics, graph data processing) and includes extract, transform, load (ETL) capabilities
SAP_HANA
travel, tourism, insurance
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