Everything about Dual graph
Graph representing faces of another graph
In the mathematical discipline of graph theory, the dual graph of a planar graph G is a graph that has a vertex for each face of G. The dual graph has an edge for each pair of faces in G that are separated from each other by an edge, and a self-loop when the same face appears on both sides of an edge. Thus, each edge e of G has a corresponding dual edge, whose endpoints are the dual vertices corresponding to the faces on either side of e. The definition of the dual depends on the choice of embedding of the graph G, so it is a property of plane graphs rather than planar graphs. For planar graphs generally, there may be multiple dual graphs, depending on the choice of planar embedding of the graph. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Dual graphA 5-minute orientation
- Skim a recent paper: Unraveling the dual defect sites in graphite carbon nitride for ultra-high photocatalytic H 2 O 2 evolutionInfluential work since 2022
- Pick up a classic book: Data structures and algorithm analysis in CThe most-reprinted book on the subject
- Read the landmark paper: Sulfur and Nitrogen Dual‐Doped Mesoporous Graphene Electrocatalyst for Oxygen Reduction with Synergistically Enhanced PerformanceCited 2,024 times
- Go sideways: Spanning treeA closely related topic
- Go sideways: Graphic matroidA closely related topic
📖 Definitions
Noun A graph derived from some plane graph in such a way that the derived graph has a vertex corresponding to each face of the given graph, an edge corresponding to each edge of the given graph that is shared by a pair of distinct faces, and a self-loop for each edge of the given graph that is a border of the same face on both of its sides.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Sulfur and Nitrogen Dual‐Doped Mesoporous Graphene Electrocatalyst for Oxygen Reduction with Synergistically Enhanced Performance
Deep Graph Clustering via Dual Correlation Reduction
Dual Quaternion Knowledge Graph Embeddings
Building irregular pyramids by dual-graph contraction
Dual graph representation of transport networks
Dual Feature Interaction-Based Graph Convolutional Network
Dual Graph Regularized Dictionary Learning
Dual-graph regularized concept factorization for clustering
🆕 Influential since 2022
Unraveling the dual defect sites in graphite carbon nitride for ultra-high photocatalytic H 2 O 2 evolution
Power Distribution Network Topology Detection Using Dual-Graph Structure Graph Neural Network Model
Dual Contrastive Learning Network for Graph Clustering
Dual Label-Guided Graph Refinement for Multi-View Graph Clustering
Dual-LightGCN: Dual light graph convolutional network for discriminative recommendation
📚 Books worth reading
Data structures and algorithm analysis in CMark Allen Weiss · 1993- 📕Dual NotebookDreaming Spirits Dreaming Spirits Publishing · 2018
- 📕Exponential random graph models for social networksDean Lusher, Johan Koskinen · 2012
Graph theory with applications to engineering and computer scienceNarsingh Deo, Narsingh Deo · 1974- 📕Dual Notebook : Graph and LinedLorie Dizon · 2018
Convergence structures and applications to functional analysisR. Beattie, H.-P. Butzmann · 2002
Information Processing in Medical ImagingJames C. Gee · 2013- 📕Dual Graph and Lined PaperDivided by Design · 2019
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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