Definition:Undirected Graph

Definition
An undirected graph is a graph whose edge set considered as a relation is symmetric.

That is, if $G$ is an undirected graph and $e = u v$ is an edge in $G$, then $v u$ is also an edge in $G$.

In other words, if you can "go from $u$ to $v$", you can also "go from $v$ to $u$".

Also see

 * Definition:Directed Graph: a graph whose edges (or arcs) have a direction, and such freedom is not guaranteed.