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An undirected incidence graph with a vertex set and an edge set; loops and parallel edges are allowed.
This atlas uses a broad incidence/multigraph convention. A simple graph is the loopless, no-parallel-edge specialization.
wp-graphnlab-graphdiestel-graph-theoryEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Add a collection of edges with endpoints in the vertex set.
Equip an existing carrier or structured object with additional chosen data, when such compatible data exists. Use a construction junction when several independently meaningful inputs must coexist on the same carrier or interact compatibly.
wp-graphnlab-graphdiestel-graph-theoryEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Require the existence of a vertex bipartition with every edge crossing between the two parts.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-bipartitediestel-graph-theoryThis is an authored directed relation from the source endpoint to the target endpoint.
Require no undirected cycles.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-forest-graphdiestel-graph-theoryThis is an authored directed relation from the source endpoint to the target endpoint.
For undirected multigraphs an isomorphism preserves the vertex-edge incidence relation and therefore respects loops and edge multiplicities when those are part of the chosen graph model.
The target represents a state, property, observable, or state-dependent description associated with the source system or theory.
diestel-graph-theoryThis is an authored directed relation from the source endpoint to the target endpoint.
A molecular graph specializes graph structure with chemical vertex and edge labels for selected atoms and bonds; it deliberately omits coordinates and most electronic information.
A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.
wp-graphdiestel-graph-theorywp-chem-molecular-graphpubchem-docsThis is an authored directed relation from the source endpoint to the target endpoint.
Require the graph to admit an embedding in the plane with edges meeting only at common endpoints.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-planardiestel-graph-theoryThis is an authored directed relation from the source endpoint to the target endpoint.
Restrict the broad incidence graph to loopless graphs with at most one edge occurrence per unordered vertex pair.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-simple-graphdiestel-graph-theoryThis is an authored directed relation from the source endpoint to the target endpoint.
Add a weight function on edges or vertices.
Equip an existing carrier or structured object with additional chosen data, when such compatible data exists. Use a construction junction when several independently meaningful inputs must coexist on the same carrier or interact compatibly.
wp-weighted-graphdiestel-graph-theory