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# Source code for networkx.algorithms.time_dependent

    """Time dependent algorithms."""

    import networkx as nx
    from networkx.utils import not_implemented_for

    __all__ = ["cd_index"]

    @not_implemented_for("undirected")
    @not_implemented_for("multigraph")
    @nx._dispatchable(node_attrs={"time": None, "weight": 1})
    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)