code: def cd_index(G, node, time_delta, *, time="time", weight=None):
      r"""Compute the CD index for `node` within the graph `G`.
  
      Calculates the CD index for the given node of the graph,
      considering only its predecessors who have the `time` attribute
      smaller than or equal to the `time` attribute of the `node`
      plus `time_delta`.
  
      Parameters
      ----------
      G : graph
         A directed networkx graph whose nodes have `time` attributes and optionally
         `weight` attributes (if a weight is not given, it is considered 1).
      node : node
         The node for which the CD index is calculated.
      time_delta : numeric or timedelta
         Amount of time after the `time` attribute of the `node`. The value of
         `time_delta` must support comparison with the `time` node attribute. For
         example, if the `time` attribute of the nodes are `datetime.datetime`
         objects, then `time_delta` should be a `datetime.timedelta` object.
      time : string (Optional, default is "time")
          The name of the node attribute that will be used for the calculations.
      weight : string (Optional, default is None)
          The name of the node attribute used as weight.
  
      Returns
      -------
      float
         The CD index calculated for the node `node` within the graph `G`.
  
      Raises
      ------
      NetworkXError
         If not all nodes have a `time` attribute or
         `time_delta` and `time` attribute types are not compatible or
         `n` equals 0.
  
      NetworkXNotImplemented
          If `G` is a non-directed graph or a multigraph.
  
      Examples
      --------
      >>> from datetime import datetime, timedelta
      >>> G = nx.DiGraph()
      >>> nodes = {
      ...     1: {"time": datetime(2015, 1, 1)},
      ...     2: {"time": datetime(2012, 1, 1), 'weight': 4},
      ...     3: {"time": datetime(2010, 1, 1)},
      ...     4: {"time": datetime(2008, 1, 1)},
      ...     5: {"time": datetime(2014, 1, 1)}
      ... }
      >>> G.add_nodes_from([(n, nodes[n]) for n in nodes])
      >>> edges = [(1, 3), (1, 4), (2, 3), (3, 4), (3, 5)]
      >>> G.add_edges_from(edges)
      >>> delta = timedelta(days=5 * 365)
      >>> nx.cd_index(G, 3, time_delta=delta, time="time")
      0.5
      >>> nx.cd_index(G, 3, time_delta=delta, time="time", weight="weight")
      0.12
  
      Integers can also be used for the time values:
      >>> node_times = {1: 2015, 2: 2012, 3: 2010, 4: 2008, 5: 2014}
      >>> nx.set_node_attributes(G, node_times, "new_time")
      >>> nx.cd_index(G, 3, time_delta=4, time="new_time")
      0.5
      >>> nx.cd_index(G, 3, time_delta=4, time="new_time", weight="weight")
      0.12
  
      Notes
      -----
      This method implements the algorithm for calculating the CD index,
      as described in the paper by Funk and Owen-Smith [1]_. The CD index
      is used in order to check how consolidating or destabilizing a patent
      is, hence the nodes of the graph represent patents and the edges show
      the citations between these patents. The mathematical model is given
      below:
  
      .. math::
          CD_{t}=\frac{1}{n_{t}}\sum_{i=1}^{n}\frac{-2f_{it}b_{it}+f_{it}}{w_{it}},
  
      where `f_{it}` equals 1 if `i` cites the focal patent else 0, `b_{it}` equals
      1 if `i` cites any of the focal patents successors else 0, `n_{t}` is the number
      of forward citations in `i` and `w_{it}` is a matrix of weight for patent `i`
      at time `t`.
  
      The `datetime.timedelta` package can lead to off-by-one issues when converting
      from years to days. In the example above `timedelta(days=5 * 365)` looks like
      5 years, but it isn't because of leap year days. So it gives the same result
      as `timedelta(days=4 * 365)`. But using `timedelta(days=5 * 365 + 1)` gives
      a 5 year delta **for this choice of years** but may not if the 5 year gap has
      more than 1 leap year. To avoid these issues, use integers to represent years,
      or be very careful when you convert units of time.
  
      References
      ----------
      .. [1] Funk, Russell J., and Jason Owen-Smith.
             "A dynamic network measure of technological change."
             Management science 63, no. 3 (2017): 791-817.
             http://russellfunk.org/cdindex/static/papers/funk_ms_2017.pdf
  
      """
      if not all(time in G.nodes[n] for n in G):
          raise nx.NetworkXError(
              "Not all nodes have a 'time' attribute."
          )
  
      try:
          # get target_date
          target_date = G.nodes[node][time] + time_delta
          # keep the predecessors that existed before the target date
          pred = {
              i for i in G.pred[node] if G.nodes[i][time] <= target_date
          }
      except:
          raise nx.NetworkXError(
              "Addition and comparison are not supported between 'time_delta' "
              "and 'time' types."
          )
  
      # -1 if any edge between node's predecessors and node's successors, else 1
      b = [-1 if any(j in G[i] for j in G[node]) else 1 for i in pred]
  
      # n is size of the union of the focal node's predecessors and its successors' predecessors
      n = len(pred.union(*(G.pred[s].keys() - {node} for s in G[node])))
      if n == 0:
          raise nx.NetworkXError("The cd index cannot be defined.")
  
      # calculate cd index
      if weight is None:
          return round(sum(bi for bi in b) / n, 2)
      else:
          # If a node has the specified weight attribute, its weight is used in the calculation
          # otherwise, a weight of 1 is assumed for that node
          weights = [G.nodes[i].get(weight, 1) for i in pred]
          return round(
              sum(bi / wt for bi, wt in zip(b, weights)) / n, 2
          )
  
label_desc: Use image node_id 1 for calling a global function with example usage: cd_index(G, node, time_delta) and returns: round, round