Is there a way to create a single edge on a graph that connects 3 or more nodes? For example, let's say that the probability of Y occurring after X is 0.1, and the probability of Z occurring after Y is 0.001, but the probability of Z occurring after both X and Y occur is 0.95. If the probabilities are assigned to each edge as weights, how can I make this happen?
$$X _\overrightarrow{0.1} Y$$
$$Y _\overrightarrow{0.001} Z$$
$$\overrightarrow{X \underrightarrow{} Y \underrightarrow{0.95}} Z$$
When edges connect more than two nodes, you don't have a graph, you have a hypergraph. More precisely, since transitions are oriented (you're starting from a digraph) and there are probability on each transition, you have a weighted hyperdigraph. I'm not sure having this term will help you that much: as data structures go, this isn't that much of a classic.
Transitions with multiple origins rather remind me of Petri nets. If your probabilities are rational numbers and there are no loops, you can scale them to integers. Otherwise you would need to reach for probabilistic Petri nets, I think.
Based on your above comments with @Gilles, what you describe is just a higher order markov model. For example an $n$th order markov model, is a model which assumes
$$ P(x_t | x_{t-1}, x_{t-2}, \ldots x_1) = P(x_t | x_{t-1}, x_{t-2}, \ldots x_{t-n}).$$
If $n$ is not fixed you have a variable order markv model.
