Definition:Undirected Graph

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 $$G$$.

vIn 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.