Knots occur in all kinds of systems, including graphs. We're used to finding knots in loops, but what about knotted theta curves? Or knotted graphs? In this talk, we discuss a general framework for constructing random embeddings of arbitrary graphs. This is a conditional probability problem, but setting up the conditions correctly requires some ideas from algebraic topology. We'll view the problem as embedding a simplicial 1-complex and see that the embedding data is (in a precise sense) dual to the simplicial homology of the 1-complex. This will enable us to make some new exact calculations for random knots.