How to find cut edges between two partitions in a graph using Python?

regarding your questions:

1. it's a correct way implementing in O(E) since in in set takes O(1) cause of hash table.

2. there are many built-in functions in NetworkX such edgeboundary(G1, group1, group2) , and you could use them in code :

   import networkx as nx
   G = nx.Graph()
   edges = [(1, 2), (1, 3), (2, 3), (4, 5), (5, 6), (4, 6), (7, 8),
            (8, 9), (9, 7), (10, 11), (3, 4), (6, 7), (9, 10)]
   G.addedgesfrom(edges)
   group1 = {1, 2, 3, 4, 5}
   group2 = {6, 7, 8, 9, 10, 11}
   cutedges = list(nx.edgeboundary(G, group1, group2))
   print(cutedges)
   

3. to automatically find balanced partitions use the graph partitioning algorithms

   maxflow-mincut-theorem, Minimum Cut - Stoer–Wagner algorithm and Multilevel partitioning (METIS)