Difference between hyper graph to bipartite graph What is the difference between a bipartite graph and a hypergraph?
Can I assume that a directed hypergraph is also a directed bipartie graph?
 A: A hypergraph is a generalisation of a graph, with hyperedges which might not contain exactly two vertices, as edges do in a graph.  A bipartite graph is a special kind of a graph.
Thus, we might write $$\text{bipartite graphs} \subsetneq \text{graphs} \subsetneq \text{hypergraphs}.$$
E.g. any hypergraph with a hyperedge that contains $3$ vertices is not even a graph, and thus not a bipartite graph.
In general, a directed hypergraph would look nothing like a directed bipartite graph.

Actually, I think I might have an idea why this question would be asked.
In something like a chemical reaction network, a directed hyperedge has multiple inputs and multiple outputs.  If we had chemical reactants $\{a,b,c\}$ and chemical products $\{X,Y\}$, then we have the directed hyperedge $(\{a,b,c\},\{X,Y\})$.  We can turn this directed hyperedge into the six directed edges $\{aX,aY,bX,bY,cX,cY\}$.
By replacing every directed hyperedge in this manner, we can obtain a directed bipartite graph.  (This came up once in my research into biological neural networks, and the massive increase in edge density as a result of this operation thwarted my analysis.)
However, it seems difficult to define a reverse process; it would require the detection of directed bicliques (and it's not even clear that the process would be reversible).
