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 $e = uv$ is an edge in $G$, then $vu$ is also an edge in $G$.

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

Compare with a directed graph, or digraph, whose edges (or arcs have a "direction", and such freedom is not guaranteed.