code: def single_source_bellman_ford(
      G, source, target=None, weight="weight"
  ):
      """Compute shortest paths and lengths in a weighted graph G.
  
      Uses Bellman-Ford algorithm for shortest paths.
  
      Parameters
      ----------
      G : NetworkX graph
  
      source : node label
          Starting node for path
  
      target : node label, optional
          Ending node for path
  
      weight : string or function
          If this is a string, then edge weights will be accessed via the
          edge attribute with this key (that is, the weight of the edge
          joining `u` to `v` will be ``G.edges[u, v][weight]``). If no
          such edge attribute exists, the weight of the edge is assumed to
          be one.
  
          If this is a function, the weight of an edge is the value
          returned by the function. The function must accept exactly three
          positional arguments: the two endpoints of an edge and the
          dictionary of edge attributes for that edge. The function must
          return a number.
  
      Returns
      -------
      distance, path : pair of dictionaries, or numeric and list
          If target is None, returns a tuple of two dictionaries keyed by node.
          The first dictionary stores distance from one of the source nodes.
          The second stores the path from one of the sources to that node.
          If target is not None, returns a tuple of (distance, path) where
          distance is the distance from source to target and path is a list
          representing the path from source to target.
  
      Raises
      ------
      NodeNotFound
          If `source` is not in `G`.
  
      Examples
      --------
      >>> G = nx.path_graph(5)
      >>> length, path = nx.single_source_bellman_ford(G, 0)
      >>> length[4]
      4
      >>> for node in [0, 1, 2, 3, 4]:
      ...     print(f"{node}: {length[node]}")
      0: 0
      1: 1
      2: 2
      3: 3
      4: 4
      >>> path[4]
      [0, 1, 2, 3, 4]
      >>> length, path = nx.single_source_bellman_ford(G, 0, 1)
      >>> length
      1
      >>> path
      [0, 1]
  
      Notes
      -----
      Edge weight attributes must be numerical.
      Distances are calculated as sums of weighted edges traversed.
  
      See Also
      --------
      single_source_dijkstra
      single_source_bellman_ford_path
      single_source_bellman_ford_path_length
      """
      if source == target:
          if source not in G:
              raise nx.NodeNotFound(
                  f"Node {source} is not found in the graph"
              )
          return (0, [source])
  
      weight = _weight_function(G, weight)
  
      paths = {source: [source]}  # dictionary of paths
      dist = _bellman_ford(
          G, [source], weight, paths=paths, target=target
      )
      if target is None:
          return (dist, paths)
      try:
          return (dist[target], paths[target])
      except KeyError as err:
          msg = f"Node {target} not reachable from {source}"
          raise nx.NetworkXNoPath(msg) from err
  
imports: from collections import deque
  from heapq import heappop, heappush
  from itertools import count
  import networkx
  from networkx.algorithms.shortest_paths.generic import _build_paths_from_predecessors
label_desc: Use image node_id 23 for calling a global function with example usage: single_source_bellman_ford(G, source, target, weight) and returns: int,  list, dist,  paths, dist,  paths