Coverage for /pythoncovmergedfiles/medio/medio/usr/local/lib/python3.9/dist-packages/networkx/algorithms/time_dependent.py: 32%
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« prev ^ index » next coverage.py v7.3.2, created at 2023-10-20 07:00 +0000
1"""Time dependent algorithms."""
3import networkx as nx
4from networkx.utils import not_implemented_for
6__all__ = ["cd_index"]
9@not_implemented_for("undirected")
10@not_implemented_for("multigraph")
11@nx._dispatch(node_attrs={"time": None, "weight": 1})
12def cd_index(G, node, time_delta, *, time="time", weight=None):
13 r"""Compute the CD index for `node` within the graph `G`.
15 Calculates the CD index for the given node of the graph,
16 considering only its predecessors who have the `time` attribute
17 smaller than or equal to the `time` attribute of the `node`
18 plus `time_delta`.
20 Parameters
21 ----------
22 G : graph
23 A directed networkx graph whose nodes have `time` attributes and optionally
24 `weight` attributes (if a weight is not given, it is considered 1).
25 node : node
26 The node for which the CD index is calculated.
27 time_delta : numeric or timedelta
28 Amount of time after the `time` attribute of the `node`. The value of
29 `time_delta` must support comparison with the `time` node attribute. For
30 example, if the `time` attribute of the nodes are `datetime.datetime`
31 objects, then `time_delta` should be a `datetime.timedelta` object.
32 time : string (Optional, default is "time")
33 The name of the node attribute that will be used for the calculations.
34 weight : string (Optional, default is None)
35 The name of the node attribute used as weight.
37 Returns
38 -------
39 float
40 The CD index calculated for the node `node` within the graph `G`.
42 Raises
43 ------
44 NetworkXError
45 If not all nodes have a `time` attribute or
46 `time_delta` and `time` attribute types are not compatible or
47 `n` equals 0.
49 NetworkXNotImplemented
50 If `G` is a non-directed graph or a multigraph.
52 Examples
53 --------
54 >>> from datetime import datetime, timedelta
55 >>> G = nx.DiGraph()
56 >>> nodes = {
57 ... 1: {"time": datetime(2015, 1, 1)},
58 ... 2: {"time": datetime(2012, 1, 1), 'weight': 4},
59 ... 3: {"time": datetime(2010, 1, 1)},
60 ... 4: {"time": datetime(2008, 1, 1)},
61 ... 5: {"time": datetime(2014, 1, 1)}
62 ... }
63 >>> G.add_nodes_from([(n, nodes[n]) for n in nodes])
64 >>> edges = [(1, 3), (1, 4), (2, 3), (3, 4), (3, 5)]
65 >>> G.add_edges_from(edges)
66 >>> delta = timedelta(days=5 * 365)
67 >>> nx.cd_index(G, 3, time_delta=delta, time="time")
68 0.5
69 >>> nx.cd_index(G, 3, time_delta=delta, time="time", weight="weight")
70 0.12
72 Integers can also be used for the time values:
73 >>> node_times = {1: 2015, 2: 2012, 3: 2010, 4: 2008, 5: 2014}
74 >>> nx.set_node_attributes(G, node_times, "new_time")
75 >>> nx.cd_index(G, 3, time_delta=4, time="new_time")
76 0.5
77 >>> nx.cd_index(G, 3, time_delta=4, time="new_time", weight="weight")
78 0.12
80 Notes
81 -----
82 This method implements the algorithm for calculating the CD index,
83 as described in the paper by Funk and Owen-Smith [1]_. The CD index
84 is used in order to check how consolidating or destabilizing a patent
85 is, hence the nodes of the graph represent patents and the edges show
86 the citations between these patents. The mathematical model is given
87 below:
89 .. math::
90 CD_{t}=\frac{1}{n_{t}}\sum_{i=1}^{n}\frac{-2f_{it}b_{it}+f_{it}}{w_{it}},
92 where `f_{it}` equals 1 if `i` cites the focal patent else 0, `b_{it}` equals
93 1 if `i` cites any of the focal patents successors else 0, `n_{t}` is the number
94 of forward citations in `i` and `w_{it}` is a matrix of weight for patent `i`
95 at time `t`.
97 The `datetime.timedelta` package can lead to off-by-one issues when converting
98 from years to days. In the example above `timedelta(days=5 * 365)` looks like
99 5 years, but it isn't because of leap year days. So it gives the same result
100 as `timedelta(days=4 * 365)`. But using `timedelta(days=5 * 365 + 1)` gives
101 a 5 year delta **for this choice of years** but may not if the 5 year gap has
102 more than 1 leap year. To avoid these issues, use integers to represent years,
103 or be very careful when you convert units of time.
105 References
106 ----------
107 .. [1] Funk, Russell J., and Jason Owen-Smith.
108 "A dynamic network measure of technological change."
109 Management science 63, no. 3 (2017): 791-817.
110 http://russellfunk.org/cdindex/static/papers/funk_ms_2017.pdf
112 """
113 if not all(time in G.nodes[n] for n in G):
114 raise nx.NetworkXError("Not all nodes have a 'time' attribute.")
116 try:
117 # get target_date
118 target_date = G.nodes[node][time] + time_delta
119 # keep the predecessors that existed before the target date
120 pred = {i for i in G.pred[node] if G.nodes[i][time] <= target_date}
121 except:
122 raise nx.NetworkXError(
123 "Addition and comparison are not supported between 'time_delta' "
124 "and 'time' types."
125 )
127 # -1 if any edge between node's predecessors and node's successors, else 1
128 b = [-1 if any(j in G[i] for j in G[node]) else 1 for i in pred]
130 # n is size of the union of the focal node's predecessors and its successors' predecessors
131 n = len(pred.union(*(G.pred[s].keys() - {node} for s in G[node])))
132 if n == 0:
133 raise nx.NetworkXError("The cd index cannot be defined.")
135 # calculate cd index
136 if weight is None:
137 return round(sum(bi for bi in b) / n, 2)
138 else:
139 # If a node has the specified weight attribute, its weight is used in the calculation
140 # otherwise, a weight of 1 is assumed for that node
141 weights = [G.nodes[i].get(weight, 1) for i in pred]
142 return round(sum(bi / wt for bi, wt in zip(b, weights)) / n, 2)