+ jRt^RIt^RIHtR.t]!R4]!R4]P !RRR^/R7RRRR/R l444tR#) zTime dependent algorithms.N)not_implemented_forcd_index undirected multigraphtimeweight) node_attrsc :aaaa\;QJd VV3RlS4F 'dK RM RM!VV3RlS44'g\P!R4hSPS,S,V,pSPS,Uu0uF&pSPV,S,V8:gK$VkK( ppTUau.uFWo\ ;QJd'TT3RlSS,4F 'gK RM RM!TT3RlSS,44'dR M^NKY pp\ TP!TT3RlSS,4!4p T ^8Xd\P!R4hTf$\\R T44T , ^4#TUu.uF&pSPT,PT^4NK( p p\\R \Y444T , ^4#uupi \P!R4h;iuupiuupi) aCompute 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 c3P<"TFpSSPV,9xK R#5iN)nodes).0nGrs& c/home/luca/screen-checking/.venv/lib/python3.14/site-packages/networkx/algorithms/time_dependent.py cd_index..qs-1atqwwqz!1s#&FTz&Not all nodes have a 'time' attribute.zPAddition and comparison are not supported between 'time_delta' and 'time' types.c3:<"TFqSS,9xK R#5ir )r jris& rrrs.g!9gsc3v<"TF.pSPV,P4S0, xK0 R#5ir )predkeys)r srnodes& rrrs*DGq)TF22Gs69zThe cd index cannot be defined.c3$"TFqxK R#5ir r)r bis& rrrs(aasc36"TFwrW, xK R#5ir r)r rwts& rrrs?VRs) allnx NetworkXErrorr ranylenunionroundsumgetzip) rr time_deltarr target_daterrbrweightss ff&d$ ` rrr sP 3-1-333-1- - -GHH  ggdmD)J6 66$<K>&!,d;S?s1??!CQGG-L    Er5sm . ,\"\"fdHa89BH&BHBH:##BHr4