  We introduce \textit{dual graph diagrams} representing oriented knots and
links. We use these combinatorial structures to define corresponding algebraic
structures we call \textit{biquasiles} whose axioms are motivated by dual graph
Reidemeister moves, generalizing the Dehn presentation of the knot group
analogously to the way quandles and biquandles generalize the Wirtinger
presentation. We use these structures to define invariants of oriented knots
and links and provide examples.
