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A vertex set and an arrow set equipped with source and target maps; loops and parallel arrows are allowed.
This is a quiver (also called a directed multigraph), not the simple-digraph convention in which an edge is merely an ordered pair of vertices.
wp-directed-graphdiestel-graph-theoryEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Use sets of vertices and arrows with source and target maps.
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-directed-graphdiestel-graph-theoryThis is an authored directed relation from the source endpoint to the target endpoint.
Retain objects as vertices, morphisms as arrows, and the source/target maps. Parallel arrows and loops remain.
Pass canonically from a stronger object to structure it determines, or forget part of the data while retaining a valid weaker structure. The carrier may change under a canonical induced construction.
wp-categorynlab-categorystacks-categorieswp-directed-graphdiestel-graph-theoryEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Require no directed cycle.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-dagdiestel-graph-theoryThis is an authored directed relation from the source endpoint to the target endpoint.
Require no loops and, for each pair of distinct vertices, exactly one of the two possible directed edges.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-tournamentdiestel-graph-theory