Algorithm to convert many instances of unidirectional lists to a graph?
You can find the smallest graph that is consistent with those walks from the graph as follows: start with an empty graph; for each pair of vertices that are adjacent in a list, e.g., $A \to B$, add the corresponding edge $A \to B$ to the graph.  The resulting graph is one that could have led to those walks, and is the smallest such.
You can't guarantee to uniquely and correctly reconstruct the original graph.  If you are unlucky, there could be some vertex in the graph that was just never visited by any walk, and then it won't appear in the reconstruction.  If walks are chosen randomly and you have enough of them, the probability of this happening might be low enough that you are willing to accept this risk.