Editing Vertex (graph theory) (section)

{{Short description|Fundamental unit of which graphs are formed}}
{{Other uses|Vertex (disambiguation)}}
{{more footnotes|date=February 2014}}

[[Image:6n-graf.svg|thumb|A graph with 6 vertices and 7 edges where the vertex number 6 on the far-left is a leaf vertex or a pendant vertex]]
In [[discrete mathematics]], and more specifically in [[graph theory]], a '''vertex''' (plural '''vertices''') or '''node''' is the fundamental unit of which graphs are formed: an [[Graph (discrete mathematics)#Graph|undirected graph]] consists of a set of vertices and a set of [[Edge (graph theory)|edges]] (unordered pairs of vertices), while a [[directed graph]] consists of a set of vertices and a set of arcs (ordered pairs of vertices).  In a diagram of a graph, a vertex is usually represented by a circle with a label, and an edge is represented by a line or arrow extending from one vertex to another.

From the point of view of graph theory, vertices are treated as featureless and indivisible [[Mathematical object|objects]], although they may have additional structure depending on the application from which the graph arises; for instance, a [[semantic network]] is a graph in which the vertices represent concepts or classes of objects.

The two vertices forming an edge are said to be the endpoints of this edge, and the edge is said to be incident to the vertices. A vertex ''w'' is said to be adjacent to another vertex ''v'' if the graph contains an edge (''v'',''w''). The [[neighborhood (graph theory)|neighborhood]] of a vertex ''v'' is an [[induced subgraph]] of the graph, formed by all vertices adjacent to&nbsp;''v''.