code: def minimum_st_edge_cut(
      G, s, t, flow_func=None, auxiliary=None, residual=None
  ):
      """Returns the edges of the cut-set of a minimum (s, t)-cut.
  
      This function returns the set of edges of minimum cardinality that,
      if removed, would destroy all paths among source and target in G.
      Edge weights are not considered. See :meth:`minimum_cut` for
      computing minimum cuts considering edge weights.
  
      Parameters
      ----------
      G : NetworkX graph
  
      s : node
          Source node for the flow.
  
      t : node
          Sink node for the flow.
  
      auxiliary : NetworkX DiGraph
          Auxiliary digraph to compute flow based node connectivity. It has
          to have a graph attribute called mapping with a dictionary mapping
          node names in G and in the auxiliary digraph. If provided
          it will be reused instead of recreated. Default value: None.
  
      flow_func : function
          A function for computing the maximum flow among a pair of nodes.
          The function has to accept at least three parameters: a Digraph,
          a source node, and a target node. And return a residual network
          that follows NetworkX conventions (see :meth:`maximum_flow` for
          details). If flow_func is None, the default maximum flow function
          (:meth:`edmonds_karp`) is used. See :meth:`node_connectivity` for
          details. The choice of the default function may change from version
          to version and should not be relied on. Default value: None.
  
      residual : NetworkX DiGraph
          Residual network to compute maximum flow. If provided it will be
          reused instead of recreated. Default value: None.
  
      Returns
      -------
      cutset : set
          Set of edges that, if removed from the graph, will disconnect it.
  
      See also
      --------
      :meth:`minimum_cut`
      :meth:`minimum_node_cut`
      :meth:`minimum_edge_cut`
      :meth:`stoer_wagner`
      :meth:`node_connectivity`
      :meth:`edge_connectivity`
      :meth:`maximum_flow`
      :meth:`edmonds_karp`
      :meth:`preflow_push`
      :meth:`shortest_augmenting_path`
  
      Examples
      --------
      This function is not imported in the base NetworkX namespace, so you
      have to explicitly import it from the connectivity package:
  
      >>> from networkx.algorithms.connectivity import minimum_st_edge_cut
  
      We use in this example the platonic icosahedral graph, which has edge
      connectivity 5.
  
      >>> G = nx.icosahedral_graph()
      >>> len(minimum_st_edge_cut(G, 0, 6))
      5
  
      If you need to compute local edge cuts on several pairs of
      nodes in the same graph, it is recommended that you reuse the
      data structures that NetworkX uses in the computation: the
      auxiliary digraph for edge connectivity, and the residual
      network for the underlying maximum flow computation.
  
      Example of how to compute local edge cuts among all pairs of
      nodes of the platonic icosahedral graph reusing the data
      structures.
  
      >>> import itertools
      >>> # You also have to explicitly import the function for
      >>> # building the auxiliary digraph from the connectivity package
      >>> from networkx.algorithms.connectivity import build_auxiliary_edge_connectivity
      >>> H = build_auxiliary_edge_connectivity(G)
      >>> # And the function for building the residual network from the
      >>> # flow package
      >>> from networkx.algorithms.flow import build_residual_network
      >>> # Note that the auxiliary digraph has an edge attribute named capacity
      >>> R = build_residual_network(H, "capacity")
      >>> result = dict.fromkeys(G, dict())
      >>> # Reuse the auxiliary digraph and the residual network by passing them
      >>> # as parameters
      >>> for u, v in itertools.combinations(G, 2):
      ...     k = len(minimum_st_edge_cut(G, u, v, auxiliary=H, residual=R))
      ...     result[u][v] = k
      >>> all(result[u][v] == 5 for u, v in itertools.combinations(G, 2))
      True
  
      You can also use alternative flow algorithms for computing edge
      cuts. For instance, in dense networks the algorithm
      :meth:`shortest_augmenting_path` will usually perform better than
      the default :meth:`edmonds_karp` which is faster for sparse
      networks with highly skewed degree distributions. Alternative flow
      functions have to be explicitly imported from the flow package.
  
      >>> from networkx.algorithms.flow import shortest_augmenting_path
      >>> len(minimum_st_edge_cut(G, 0, 6, flow_func=shortest_augmenting_path))
      5
  
      """
      if flow_func is None:
          flow_func = default_flow_func
  
      if auxiliary is None:
          H = build_auxiliary_edge_connectivity(G)
      else:
          H = auxiliary
  
      kwargs = {
          "capacity": "capacity",
          "flow_func": flow_func,
          "residual": residual,
      }
  
      cut_value, partition = nx.minimum_cut(H, s, t, **kwargs)
      reachable, non_reachable = partition
      # Any edge in the original graph linking the two sets in the
      # partition is part of the edge cutset
      cutset = set()
      for u, nbrs in ((n, G[n]) for n in reachable):
          cutset.update((u, v) for v in nbrs if v in non_reachable)
  
      return cutset
  
file_path: networkx/networkx/algorithms/connectivity/cuts.py
imports: import itertools
  import networkx
  from networkx.algorithms.flow import build_residual_network, edmonds_karp
  from .utils import build_auxiliary_edge_connectivity, build_auxiliary_node_connectivity
label_desc: Use image node_id 1 for calling a global function with example usage: minimum_st_edge_cut(G, s, t, flow_func, auxiliary, residual) and returns: cutset