code: def min_fill_in_heuristic(graph):
      """Implements the Minimum Degree heuristic.
  
      Returns the node from the graph, where the number of edges added when
      turning the neighborhood of the chosen node into clique is as small as
      possible. This algorithm chooses the nodes using the Minimum Fill-In
      heuristic. The running time of the algorithm is :math:`O(V^3)` and it uses
      additional constant memory."""
  
      if len(graph) == 0:
          return None
  
      min_fill_in_node = None
  
      min_fill_in = sys.maxsize
  
      # sort nodes by degree
      nodes_by_degree = sorted(graph, key=lambda x: len(graph[x]))
      min_degree = len(graph[nodes_by_degree[0]])
  
      # abort condition (handle complete graph)
      if min_degree == len(graph) - 1:
          return None
  
      for node in nodes_by_degree:
          num_fill_in = 0
          nbrs = graph[node]
          for nbr in nbrs:
              # count how many nodes in nbrs current nbr is not connected to
              # subtract 1 for the node itself
              num_fill_in += len(nbrs - graph[nbr]) - 1
              if num_fill_in >= 2 * min_fill_in:
                  break
  
          num_fill_in /= 2  # divide by 2 because of double counting
  
          if num_fill_in < min_fill_in:  # update min-fill-in node
              if num_fill_in == 0:
                  return node
              min_fill_in = num_fill_in
              min_fill_in_node = node
  
      return min_fill_in_node
  
file_path: networkx/networkx/algorithms/approximation/treewidth.py
imports: import itertools
  import sys
  from heapq import heapify, heappop, heappush
  import networkx
  from networkx.utils import not_implemented_for
label_desc: Use image node_id 3 for calling a global function with example usage: min_fill_in_heuristic(graph) and returns: min_fill_in_node, None, None, node