+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ### Context #### Graph theory +-- {: .hide} [[!include graph theory - contents]] =-- =-- =-- # Contents * table of contents {: toc} ## Idea A __vertex__ is a _[[point]]_ in a [[graph]] or [[simplicial set]] or similar. In the context of [[simplicial sets]] it is a 0-[[dimension|dimensional]] [[simplex]]. ## Terminological remarks Vertices are also sometimes called **points** (somewhat old-fashioned, e.g. [Harary, Chapter 2](#HararyGraphTheory)) or **nodes** (more frequently in [[computer science]]). In specialized contexts other terms are used. For instance, the two classes of vertices of a [[Petri net]] are called "places" or "species" and "transitions" or "reactions", respectively; in an [[automaton]] the vertices are called "states"; and for [[quasicategories]] (particular simplicial sets) the vertices are also called [[objects]]. Historically, the use of "vertex" for a point of an abstract graph probably derives from the natural connections between [[graph theory]] and the theory of [[polyhedra]], which have "vertices". One such connection is [[Ernst Steinitz|Steinitz's]] [[Steinitz's theorem|1916 theorem]] on the one-dimensional skeleta of [[polyhedra]] in three-dimensional [[Euclidean space]]. ## Related concepts * [[graph]], [[directed graph]], [[quiver]], [[digraph]] * [[simplicial set]] * [[edge]] * **vertex**, [[simplex]], [[dendrex]] ## References * Frank Harary: Graph Theory. Addison-Wesley. 1969 {#HararyGraphTheory} [[!redirects vertex]] [[!redirects vertices]] [[!redirects node]] [[!redirects nodes]]