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 $$G = \left({V, E}\right)$$ such that:
 * $$V$$ is a set;
 * $$E$$ is a set of 2-element subsets of $$V$$.

That is: $$E \subseteq \left\{{\left\{{u, v}\right\}: u, v \in V}\right\}$$

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