Definition:Graph (Graph Theory)

A graph is intuitively defined as a pair consisting of a set of nodes or vertices and a set of edges.

More precisely, a graph is an ordered pair $$G = (V,E)$$ such that $$V$$ is a set and $$E$$ is a set of 2-element subsets of $$V$$. That is: $$E \subseteq \{ \{u,v\} : u,v \in V \}$$

An edge $$e = \{u,v\} \in E$$ is said to be incident to $$u$$ and $$v$$; similarly, $$u$$ and $$v$$ are said to be adjacent or neighboring.