  We study invariants of virtual graphoids, which are virtual spatial graph
diagrams with two distinguished degree-one vertices modulo graph Reidemeister
moves applied away from the distinguished vertices. Generalizing previously
known results, we give topological interpretations of graphoids. There are
several applications to virtual graphoid theory. First, virtual graphoids are
suitable objects for studying knotted graphs with open ends arising in
proteins. Second, a virtual graphoid can be thought of as a way to represent a
virtual spatial graph without using as many crossings, which can be
advantageous for computing invariants.
