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Everything about Independence complex
The independence complex of a graph is a mathematical object describing the 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, a family of finite sets closed under the operation of taking subsets), formed by the sets of vertices in the independent sets of G. Any subset of an independent set is itself an independent set, so I(G) is indeed closed under taking subsets. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Independence complexA 5-minute orientation
- Skim a recent paper: Community based complex interventions to sustain independence in older people: systematic review and network meta-analysisInfluential work since 2022
- Pick up a classic book: A course in minimal surfacesThe most-reprinted book on the subject
- Read the landmark paper: Relationship Between Visual and Kinesthetic Imagery, Field Dependence-Independence, and Complex Motor SkillsCited 74 times
- Go sideways: Clique complexA closely related topic
- Go sideways: Meshulam's gameA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Relationship Between Visual and Kinesthetic Imagery, Field Dependence-Independence, and Complex Motor Skills
Political Power and Civil Counterpower: The Complex Dynamics of the Catalan Independence Movement
Complex Religion: Interrogating Assumptions of Independence in the Study of Religion
The complex relation between director independence and board effectiveness
Dynamical independence: Discovering emergent macroscopic processes in complex dynamical systems
The topology of the independence complex
Testing for independence in contingency tables with complex sample survey data
On the independence complex of square grids
🆕 Influential since 2022
Community based complex interventions to sustain independence in older people: systematic review and network meta-analysis
Declarations of Independence: How Embedded Multicollinearity Errors Affect Dosimetric and Other Complex Analyses in Radiation Oncology
Subdomains of the Helicobacter pylori Cag T4SS outer membrane core complex exhibit structural independence
The total Betti number of the independence complex of ternary graphs
ENGINEERING TRAINING AS A FACTOR IN ACHIEVING TECHNOLOGICAL INDEPENDENCE OF THE INDUSTRIAL COMPLEX
📚 Books worth reading
- 📕A course in minimal surfacesTobias H. Colding · 2011
- 📕Horizons of Fractal Geometry and Complex DimensionsRobert G. Niemeyer · 2019
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Clique complex Clique complexes, independence complexes, flag complexes, Whitney complexes and conformal hypergraphs are closely related mathematical objects in graph…
- Meshulam's game In graph theory, Meshulam's game is a game used to explain a theorem of Roy Meshulam related to the homological connectivity of the independence complex…
- Width of a hypergraph In graph theory, there are two related properties of a hypergraph that are called its "width". Given a hypergraph H = (V, E), we say that a set K of edges…
- Rainbow-independent set In graph theory, a rainbow-independent set (ISR) is an independent set in a graph, in which each vertex has a different color. Formally, let G = (V, E)…
- Abstract simplicial complex In combinatorics, an abstract simplicial complex (ASC), often called an abstract complex or just a complex, is a family of sets that is closed under taking…
- Hall-type theorems for hypergraphs In the mathematical field of graph theory, Hall-type theorems for hypergraphs are several generalizations of Hall's marriage theorem from graphs to hypergraphs…
- Homological connectivity In algebraic topology, homological connectivity is a property describing a topological space based on its homology groups. X is homologically-connected…
- Chessboard complex A chessboard complex is a particular kind of abstract simplicial complex, which has various applications in topological graph theory and algebraic topology…