code: def minimal_branching(
      G,
      /,
      *,
      attr="weight",
      default=1,
      preserve_attrs=False,
      partition=None,
  ):
      """
      Returns a minimal branching from `G`.
  
      A minimal branching is a branching similar to a minimal arborescence but
      without the requirement that the result is actually a spanning arborescence.
      This allows minimal branchinges to be computed over graphs which may not
      have arborescence (such as multiple components).
  
      Parameters
      ----------
      G : (multi)digraph-like
          The graph to be searched.
      attr : str
          The edge attribute used in determining optimality.
      default : float
          The value of the edge attribute used if an edge does not have
          the attribute `attr`.
      preserve_attrs : bool
          If True, preserve the other attributes of the original graph (that are not
          passed to `attr`)
      partition : str
          The key for the edge attribute containing the partition
          data on the graph. Edges can be included, excluded or open using the
          `EdgePartition` enum.
  
      Returns
      -------
      B : (multi)digraph-like
          A minimal branching.
      """
      max_weight = -INF
      min_weight = INF
      for _, _, w in G.edges(data=attr):
          if w > max_weight:
              max_weight = w
          if w < min_weight:
              min_weight = w
  
      for _, _, d in G.edges(data=True):
          # Transform the weights so that the minimum weight is larger than
          # the difference between the max and min weights. This is important
          # in order to prevent the edge weights from becoming negative during
          # computation
          d[attr] = max_weight + 1 + (max_weight - min_weight) - d[attr]
  
      B = maximum_branching(G, attr, default, preserve_attrs, partition)
  
      # Reverse the weight transformations
      for _, _, d in G.edges(data=True):
          d[attr] = max_weight + 1 + (max_weight - min_weight) - d[attr]
  
      for _, _, d in B.edges(data=True):
          d[attr] = max_weight + 1 + (max_weight - min_weight) - d[attr]
  
      return B
  
imports: import string
  from dataclasses import dataclass, field
  from enum import Enum
  from operator import itemgetter
  from queue import PriorityQueue
  import networkx
  from networkx.utils import py_random_state
  from .recognition import is_arborescence, is_branching
label_desc: Use image node_id 9 for calling a global function with example usage: minimal_branching() and returns: B