text: import networkx as nx
  from networkx.utils.decorators import py_random_state, not_implemented_for
  
  __all__ = ["randomized_partitioning", "one_exchange"]
  
  
  @not_implemented_for("directed", "multigraph")
  @py_random_state(1)
  def randomized_partitioning(G, seed=None, p=0.5, weight=None):
      """Compute a random partitioning of the graph nodes and its cut value.
  
      A partitioning is calculated by observing each node
      and deciding to add it to the partition with probability `p`,
      returning a random cut and its corresponding value (the
      sum of weights of edges connecting different partitions).
  
      Parameters
      ----------
      G : NetworkX graph
  
      seed : integer, random_state, or None (default)
          Indicator of random number generation state.
          See :ref:`Randomness<randomness>`.
  
      p : scalar
          Probability for each node to be part of the first partition.
          Should be in [0,1]
  
      weight : object
          Edge attribute key to use as weight. If not specified, edges
          have weight one.
  
      Returns
      -------
      cut_size : scalar
          Value of the minimum cut.
  
      partition : pair of node sets
          A partitioning of the nodes that defines a minimum cut.
      """
      cut = {node for node in G.nodes() if seed.random() < p}
      cut_size = nx.algorithms.cut_size(G, cut, weight=weight)
      partition = (cut, G.nodes - cut)
      return cut_size, partition
  
  
  def _swap_node_partition(cut, node):
      return cut - {node} if node in cut else cut.union({node})
  
  
  @not_implemented_for("directed", "multigraph")
  @py_random_state(2)
  def one_exchange(G, initial_cut=None, seed=None, weight=None):
      """Compute a partitioning of the graphs nodes and the corresponding cut value.
  
      Use a greedy one exchange strategy to find a locally maximal cut
      and its value, it works by finding the best node (one that gives
      the highest gain to the cut value) to add to the current cut
      and repeats this process until no improvement can be made.
  
      Parameters
      ----------
      G : networkx Graph
          Graph to find a maximum cut for.
  
      initial_cut : set
          Cut to use as a starting point. If not supplied the algorithm
          starts with an empty cut.
  
      seed : integer, random_state, or None (default)
          Indicator of random number generation state.
          See :ref:`Randomness<randomness>`.
  
      weight : object
          Edge attribute key to use as weight. If not specified, edges
          have weight one.
  
      Returns
      -------
      cut_value : scalar
          Value of the maximum cut.
  
      partition : pair of node sets
          A partitioning of the nodes that defines a maximum cut.
      """
      if initial_cut is None:
          initial_cut = set()
      cut = set(initial_cut)
      current_cut_size = nx.algorithms.cut_size(G, cut, weight=weight)
      while True:
          nodes = list(G.nodes())
          # Shuffling the nodes ensures random tie-breaks in the following call to max
          seed.shuffle(nodes)
          best_node_to_swap = max(
              nodes,
              key=lambda v: nx.algorithms.cut_size(
                  G, _swap_node_partition(cut, v), weight=weight
              ),
              default=None,
          )
          potential_cut = _swap_node_partition(cut, best_node_to_swap)
          potential_cut_size = nx.algorithms.cut_size(G, potential_cut, weight=weight)
  
          if potential_cut_size > current_cut_size:
              cut = potential_cut
              current_cut_size = potential_cut_size
          else:
              break
  
      partition = (cut, G.nodes - cut)
      return current_cut_size, partition
  