Everything about Line graph
Graph representing edges of another 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 of G. L(G) is constructed in the following way: for each edge in G, make a vertex in L(G); for every two edges in G that have a vertex in common, make an edge between their corresponding vertices in L(G). Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Line graphA 5-minute orientation
- Skim a recent paper: The emerging graph neural networks for intelligent fault diagnostics and prognostics: A guideline and a benchmark studyInfluential work since 2022
- Pick up a classic book: Wave PhenomenaThe most-reprinted book on the subject
- Read the landmark paper: Depth-First Search and Linear Graph AlgorithmsCited 4,769 times
- Go sideways: Glossary of graph theoryA closely related topic
- Go sideways: Perfect graphA closely related topic
📖 Definitions
Noun A graph in which a series of connected straight lines connect points, each of which represents the value of a particular variable as a function of another variable.
Noun A graph L(G) which is derived from a given non-oriented graph G such that the vertices of L(G) represent edges of G and so that a clique in L(G) represents a common end-vertex shared by a set of represented edges. (A star subgraph in G transforms into a clique in L(G).) A graph which is the line graph (in the above sense) of some other graph.
Noun A graph which is the line graph (in the above sense) of some other graph.
🏆 Landmark papers (most cited)
Depth-First Search and Linear Graph Algorithms
Orbital design of flat bands in non-line-graph lattices via line-graph wave functions
Subdivision Graph, Power and Line Graph of a Soft Graph
On the Line Graph of the Complete Bipartite Graph
Line graph eigenvalues and line energy of caterpillars
QSPR Modeling: Graph Connectivity Indices versus Line Graph Connectivity Indices
Parallel and On-Line Graph Coloring
Graph invariants of the line graph of zero divisor graph of $$\mathbb {Z}_{n}$$
🆕 Influential since 2022
The emerging graph neural networks for intelligent fault diagnostics and prognostics: A guideline and a benchmark study
Line graph contrastive learning for link prediction
Line graph neural networks for link weight prediction
Weak degeneracy of the square of the line graph of a subcubic graph
Line-graph-lattice crystal structures of stoichiometric materials
📚 Books worth reading
Wave PhenomenaDudley H. Towne · 1967- 📕Introduction to Analysis on GraphsAlexander Grigor'yan · 2018
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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