Create "minimally connected" directed acyclic graph

Question

I have a directed acyclic simple graph in NetworkX.

Now, for each edge, that edge has a "source" and a "target". If there exists a path from the "source" to the "target" besides this edge, then I want to delete this edge.

1. Does NetworkX have a built-in function to do this?

I really don't want to re-invent the wheel.

2. [optional] Only in the case that the answer to 1 is "no", then what is the most efficient algorithm to achieve this (for a fairly dense graph)?

Here is an example of a DAG that needs to be cleaned:

• The nodes are:

  ['termsequence', 'maximumdegree', 'emptymultigraph', 'minimum', 'multiset', 'walk', 'nonemptymultigraph', 'euleriantrail', 'nonnullmultigraph', 'cycle', 'loop', 'abwalk', 'endvertices', 'simplegraph', 'vertex', 'multipletrails', 'edge', 'set', 'stroll', 'union', 'trailcondition', 'nullmultigraph', 'trivialmultigraph', 'sequence', 'multiplepaths', 'path', 'degreevertex', 'onedgesonvertices', 'nontrivialmultigraph', 'adjacentedges', 'adjacentvertices', 'simpleedge', 'maximum', 'multipleloops', 'length', 'circuit', 'class', 'euleriangraph', 'incident', 'minimumdegree', 'orderedpair', 'unique', 'closedwalk', 'multipleedges', 'pathcondition', 'multigraph', 'trail']
  

• The edges are:

  [('termsequence', 'endvertices'), ('emptymultigraph', 'nonemptymultigraph'), ('minimum', 'minimumdegree'), ('multiset', 'trailcondition'), ('multiset', 'pathcondition'), ('multiset', 'multigraph'), ('walk', 'length'), ('walk', 'closedwalk'), ('walk', 'abwalk'), ('walk', 'trail'), ('walk', 'endvertices'), ('euleriantrail', 'euleriangraph'), ('loop', 'simplegraph'), ('loop', 'degreevertex'), ('loop', 'simpleedge'), ('loop', 'multipleloops'), ('endvertices', 'abwalk'), ('vertex', 'adjacentvertices'), ('vertex', 'onedgesonvertices'), ('vertex', 'walk'), ('vertex', 'adjacentedges'), ('vertex', 'multipleedges'), ('vertex', 'edge'), ('vertex', 'multipleloops'), ('vertex', 'degreevertex'), ('vertex', 'incident'), ('edge', 'adjacentvertices'), ('edge', 'onedgesonvertices'), ('edge', 'multipleedges'), ('edge', 'simpleedge'), ('edge', 'adjacentedges'), ('edge', 'loop'), ('edge', 'trailcondition'), ('edge', 'pathcondition'), ('edge', 'walk'), ('edge', 'incident'), ('set', 'onedgesonvertices'), ('set', 'edge'), ('union', 'multiplepaths'), ('union', 'multipletrails'), ('trailcondition', 'trail'), ('nullmultigraph', 'nonnullmultigraph'), ('sequence', 'walk'), ('sequence', 'endvertices'), ('path', 'cycle'), ('path', 'multiplepaths'), ('degreevertex', 'maximumdegree'), ('degreevertex', 'minimumdegree'), ('onedgesonvertices', 'multigraph'), ('maximum', 'maximumdegree'), ('circuit', 'euleriangraph'), ('class', 'multiplepaths'), ('class', 'multipletrails'), ('incident', 'adjacentedges'), ('incident', 'degreevertex'), ('incident', 'onedgesonvertices'), ('orderedpair', 'multigraph'), ('closedwalk', 'circuit'), ('closedwalk', 'cycle'), ('closedwalk', 'stroll'), ('pathcondition', 'path'), ('multigraph', 'euleriangraph'), ('multigraph', 'nullmultigraph'), ('multigraph', 'trivialmultigraph'), ('multigraph', 'nontrivialmultigraph'), ('multigraph', 'emptymultigraph'), ('multigraph', 'euleriantrail'), ('multigraph', 'simplegraph'), ('trail', 'path'), ('trail', 'circuit'), ('trail', 'multipletrails')]
  

Answer 1

You can use nx.transitive_reduction(G).

Here is an example in the documentation.

DG = nx.DiGraph([(1, 2), (2, 3), (1, 3)])
TR = nx.transitive_reduction(DG)
list(TR.edges)  # [(1, 2), (2, 3)]