code: def minimum_edge_cut(G, s=None, t=None, flow_func=None):
      r"""Returns a set of edges of minimum cardinality that disconnects G.
  
      If source and target nodes are provided, this function returns the
      set of edges of minimum cardinality that, if removed, would break
      all paths among source and target in G. If not, it returns a set of
      edges of minimum cardinality that disconnects G.
  
      Parameters
      ----------
      G : NetworkX graph
  
      s : node
          Source node. Optional. Default value: None.
  
      t : node
          Target node. Optional. 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 below for details. The
          choice of the default function may change from version
          to version and should not be relied on. Default value: None.
  
      Returns
      -------
      cutset : set
          Set of edges that, if removed, would disconnect G. If source
          and target nodes are provided, the set contains the edges that
          if removed, would destroy all paths between source and target.
  
      Examples
      --------
      >>> # Platonic icosahedral graph has edge connectivity 5
      >>> G = nx.icosahedral_graph()
      >>> len(nx.minimum_edge_cut(G))
      5
  
      You can use alternative flow algorithms for the underlying
      maximum flow computation. 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(nx.minimum_edge_cut(G, flow_func=shortest_augmenting_path))
      5
  
      If you specify a pair of nodes (source and target) as parameters,
      this function returns the value of local edge connectivity.
  
      >>> nx.edge_connectivity(G, 3, 7)
      5
  
      If you need to perform several local computations among different
      pairs of nodes on the same graph, it is recommended that you reuse
      the data structures used in the maximum flow computations. See
      :meth:`local_edge_connectivity` for details.
  
      Notes
      -----
      This is a flow based implementation of minimum edge cut. For
      undirected graphs the algorithm works by finding a 'small' dominating
      set of nodes of G (see algorithm 7 in [1]_) and computing the maximum
      flow between an arbitrary node in the dominating set and the rest of
      nodes in it. This is an implementation of algorithm 6 in [1]_. For
      directed graphs, the algorithm does n calls to the max flow function.
      The function raises an error if the directed graph is not weakly
      connected and returns an empty set if it is weakly connected.
      It is an implementation of algorithm 8 in [1]_.
  
      See also
      --------
      :meth:`minimum_st_edge_cut`
      :meth:`minimum_node_cut`
      :meth:`stoer_wagner`
      :meth:`node_connectivity`
      :meth:`edge_connectivity`
      :meth:`maximum_flow`
      :meth:`edmonds_karp`
      :meth:`preflow_push`
      :meth:`shortest_augmenting_path`
  
      References
      ----------
      .. [1] Abdol-Hossein Esfahanian. Connectivity Algorithms.
          http://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf
  
      """
      if (s is not None and t is None) or (s is None and t is not None):
          raise nx.NetworkXError(
              "Both source and target must be specified."
          )
  
      # reuse auxiliary digraph and residual network
      H = build_auxiliary_edge_connectivity(G)
      R = build_residual_network(H, "capacity")
      kwargs = {"flow_func": flow_func, "residual": R, "auxiliary": H}
  
      # Local minimum edge cut if s and t are not None
      if s is not None and t is not None:
          if s not in G:
              raise nx.NetworkXError(f"node {s} not in graph")
          if t not in G:
              raise nx.NetworkXError(f"node {t} not in graph")
          return minimum_st_edge_cut(H, s, t, **kwargs)
  
      # Global minimum edge cut
      # Analog to the algorithm for global edge connectivity
      if G.is_directed():
          # Based on algorithm 8 in [1]
          if not nx.is_weakly_connected(G):
              raise nx.NetworkXError("Input graph is not connected")
  
          # Initial cutset is all edges of a node with minimum degree
          node = min(G, key=G.degree)
          min_cut = set(G.edges(node))
          nodes = list(G)
          n = len(nodes)
          for i in range(n):
              try:
                  this_cut = minimum_st_edge_cut(
                      H, nodes[i], nodes[i + 1], **kwargs
                  )
                  if len(this_cut) <= len(min_cut):
                      min_cut = this_cut
              except IndexError:  # Last node!
                  this_cut = minimum_st_edge_cut(
                      H, nodes[i], nodes[0], **kwargs
                  )
                  if len(this_cut) <= len(min_cut):
                      min_cut = this_cut
  
          return min_cut
  
      else:  # undirected
          # Based on algorithm 6 in [1]
          if not nx.is_connected(G):
              raise nx.NetworkXError("Input graph is not connected")
  
          # Initial cutset is all edges of a node with minimum degree
          node = min(G, key=G.degree)
          min_cut = set(G.edges(node))
          # A dominating set is \lambda-covering
          # We need a dominating set with at least two nodes
          for node in G:
              D = nx.dominating_set(G, start_with=node)
              v = D.pop()
              if D:
                  break
          else:
              # in complete graphs the dominating set will always be of one node
              # thus we return min_cut, which now contains the edges of a node
              # with minimum degree
              return min_cut
          for w in D:
              this_cut = minimum_st_edge_cut(H, v, w, **kwargs)
              if len(this_cut) <= len(min_cut):
                  min_cut = this_cut
  
          return min_cut
  
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 4 for calling a global function with example usage: minimum_edge_cut(G, s, t, flow_func) and returns: minimum_st_edge_cut, min_cut, min_cut, min_cut