In the current graph implementation, it takes O(1) time to find the out-edges of a vertex, but O(e) time (where e is the total number of edges in the graph) to find the in-edges of a vertex.
In some scenarios (e.g. clearing cache in hep planner), this may have severe performance penalty. To solve this problem, we add a inward edge table, in addition to the existing outward edge table, to the graph. This helps to reduce the time complexity for finding in-edges to O(1).
Please note that, there is extra performance overhead for maintaining the in edge table, when adding/deleting vertices to the graph. However, the added overhead only takes O(1) time.
Finally, it should be noted that, some existing operations can benefit from this improvement (e.g. topological sort).