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Everything about Line graph of a hypergraph
Generalization of line graphs to hypergraphs
In graph theory, particularly in the theory of hypergraphs, the line graph of a hypergraph H, denoted L(H), is the graph whose vertex set is the set of the hyperedges of H, with two vertices adjacent in L(H) when their corresponding hyperedges have a nonempty intersection in H. In other words, L(H) is the intersection graph of a family of finite sets. It is a generalization of the line graph of a graph. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Line graph of a hypergraphA 5-minute orientation
- Skim a recent paper: AHD-SLE: Anomalous Hyperedge Detection on Hypergraph Symmetric Line ExpansionInfluential work since 2022
- Pick up a classic book: Thirty Essays on Geometric Graph TheoryThe most-reprinted book on the subject
- Read the landmark paper: Depth-based hypergraph complexity traces from directed line graphsCited 18 times
- Go sideways: Forbidden graph characterizationA closely related topic
- Go sideways: Line graphA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Depth-based hypergraph complexity traces from directed line graphs
Mapping ontology vertices to a line using hypergraph framework
SynergyGraph: predicting cell line specific drug combination synergy scores using knowledge graph representation and hypergraph modeling
Bipolar Fuzzy Line Graph of a Bipolar Fuzzy Hypergraph
Hamilton Cycles in the Line Graph of a Random Hypergraph
On hypergraph coloring and 3-uniform linear hypergraph set-indexers of a graph
🆕 Influential since 2022
📚 Books worth reading
Thirty Essays on Geometric Graph TheoryJános Pach · 2012- 📕Graphs, hypergraphs, and matroidsRegional Scientific Session of Mathematicians (5th 1985 Żagań, Poland) · 1985
- 📕Graphs, hypergraphs, and matroids IIM. Borowiecki, Zdzisław Skupień · 1987
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Forbidden graph characterization 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…
- Line 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…
- Matching in hypergraphs In graph theory, a matching in a hypergraph is a set of hyperedges, in which every two hyperedges are disjoint. It is an extension of the notion of matching…
- Hypergraph In mathematics, a 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…
- Vertex cover in hypergraphs In graph theory, a vertex cover in a hypergraph is a set of vertices, such that every hyperedge of the hypergraph contains at least one vertex of that…
- Erdős–Faber–Lovász conjecture Unsolved problem in mathematics Conjecture: If k complete graphs, each having exactly k vertices, have the property that every pair of complete graphs…
- Bipartite graph 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…
- Hypertree In the mathematical field of graph theory, a hypergraph H is called a hypertree if it admits a host graph T such that T is a tree. In other words, H is…