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Dual 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…

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Dual graph

Nodes164
Edges163
Triples90
Avg. degree1.99
Density0.012195
Components1

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Dual graph

Top relations

related to history · 18
Dual graph → Alfred Kempe, Cremona, Duality, Harmonices Mundi, Hassler Whitney, In, Johannes Kepler, Königsberg, Leonhard Euler's, Lothar Heffter, Nouvelle Méchanique, Pierre Varignon's, Recognizable, Seven Bridges, Statique, The, This, Varignon
related to Spanning trees · 10
Dual graph → An, But, However, If, In, Similar, Symmetrically, That, Therefore, Thus
related to Nonplanar embeddings · 9
Dual graph → For, Heawood, In, K6, K7, Petersen, The, This, With
related to Uniqueness · 9
Dual graph → Because, By Steinitz's, For, Hassler Whitney, In, K2, Moreover, The, When
related to Matroids and algebraic duals · 8
Dual graph → An, Every, Hassler Whitney, If, In, The, Then Whitney's, Whitney's
related to Self-dual graphs · 7
Dual graph → Christopher, Euler's, Every, However, It, Servatius, The
related to Cycles and dipoles · 6
Dual graph → Conversely, However, Jordan, Such, The, Therefore
related to Cuts and cycles · 5
Dual graph → In, Jordan, Removing, The, This
related to Simple graphs versus multigraphs · 5
Dual graph → As, For, The, Therefore, This
related to External links · 4
Dual graph → Dual, Eric, MathWorld, Weisstein

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Important terminology

dual graph planar graphs edges two duality cycle vertices plane connected embedding edge may simple vertex faces one spanning isomorphic

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Dual graphis atype of Cremona diagram0.90text
points of the plane that are neither part of an open region disjoint from the graph nor part of an edge or vertex of the graphinstance ofcare is needed to avoid topological complications0.80text
Dual graphrelated to Cuts and cyclesRemoving0.60section
Dual graphrelated to Cuts and cyclesIn0.60section
Dual graphrelated to Cuts and cyclesThis0.60section
Dual graphrelated to Cuts and cyclesJordan0.60section
Dual graphrelated to Cuts and cyclesThe0.60section
Dual graphrelated to Cycles and dipolesThe0.60section
Dual graphrelated to Cycles and dipolesJordan0.60section
Dual graphrelated to Cycles and dipolesHowever0.60section
Dual graphrelated to Cycles and dipolesTherefore0.60section
Dual graphrelated to Cycles and dipolesSuch0.60section

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