Live briefing
Everything about Threshold graph
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:Addition of a single isolated vertex to the graph. Addition of a single dominating vertex to the graph, i.e. a single vertex that is connected to all other vertices. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Threshold graphA 5-minute orientation
- Skim a recent paper: Topological analysis of 3D fracture networks: Graph representation and percolation thresholdInfluential work since 2022
- Pick up a classic book: Advances in Multimedia ModelingThe most-reprinted book on the subject
- Read the landmark paper: Every monotone graph property has a sharp thresholdCited 228 times
- Go sideways: Trivially perfect graphA closely related topic
- Go sideways: CographA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Every monotone graph property has a sharp threshold
The minimum degree threshold for perfect graph packings
Threshold selection in gene co-expression networks using spectral graph theory techniques
Tight Lower Bound for Percolation Threshold on an Infinite Graph
Extremal optimization of graph partitioning at the percolation threshold
Threshold Graph Limits and Random Threshold Graphs
On the adjacency matrix of a threshold graph
The critical group of a threshold graph
🆕 Influential since 2022
Topological analysis of 3D fracture networks: Graph representation and percolation threshold
Graph-Structured Convolution-Guided Continuous Context Threshold-Aware Networks for Hyperspectral Image Classification
A Rotating Machinery Fault Diagnosis Method Based on Dynamic Graph Convolution Network and Hard Threshold Denoising
A novel method for variable-speed mechanical fault diagnosis using sparse threshold graph and adaptive loss weighting
Adaptive Dynamic Threshold Graph Neural Network: A Novel Deep Learning Framework for Cross-Condition Bearing Fault Diagnosis
📚 Books worth reading
Advances in Multimedia ModelingShipeng Li · 2012
Trends and Topics in Computer VisionKiriakos N. Kutulakos · 2012
Design and Analysis of AlgorithmsGuy Even · 2012
Discovery ScienceJean-Gabriel Ganascia · 2012
Threshold graphs and related topicsN. V. R. Mahadev · 1995- 📕A Sharp threshold for random graphs with a monochromatic triangle in every edge coloringEhud Friedgut · 2006
The challenges of systems biologyGustavo Stolovitzky · 2009- 📕Recent advances in natural language processing VRANLP 2007 (2007 Borovet︠s︡, Bulgaria) · 2009
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Trivially perfect graph In graph theory, a trivially perfect graph is a graph with the property that in each of its induced subgraphs the size of the maximum independent set equals…
- Cograph In graph theory, a cograph, or complement-reducible graph, or P4-free graph, is a graph that can be generated from the single-vertex graph K1 by complementation…
- Complement graph In the mathematical field of graph theory, the complement or inverse of a graph G is a graph H on the same vertices such that two distinct vertices are…
- Perfectly orderable graph In graph theory, a perfectly orderable graph is a graph whose vertices can be ordered in such a way that a greedy coloring algorithm with that ordering…
- Perfect graph 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…
- Distance-hereditary graph In graph theory, a branch of discrete mathematics, a distance-hereditary graph (also called a completely separable graph) is a graph in which the distances…
- Perfect graph theorem In graph theory, the perfect graph theorem of László Lovász (1972a, 1972b) states that an undirected graph is perfect if and only if its complement graph…
- Skew partition In graph theory, a skew partition of a graph is a partition of its vertices into two subsets, such that the induced subgraph formed by one of the two subsets…