o ]ZŽh‚ã@sTdZddlZddlmZdgZedƒedƒejdddœd d ddœd d„ƒƒƒZdS) zTime dependent algorithms.éN)Únot_implemented_forÚcd_indexZ undirectedZ multigraphé)ÚtimeÚweight)Z node_attrsrc st‡‡fdd„ˆDƒƒst d¡‚zˆjˆˆ|‰‡‡‡fdd„ˆjˆDƒ}Wnt d¡‚‡‡fdd„|Dƒ}t|j‡‡fd d„ˆˆDƒŽƒ}|d krWt d ¡‚ˆd urittd d„|Dƒƒ|dƒS‡‡fdd„|Dƒ}ttdd„t ||ƒDƒƒ|dƒS)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 c3s|] }ˆˆj|vVqdS©N©Únodes)Ú.0Ún)ÚGr©úQ/var/www/auris/lib/python3.10/site-packages/networkx/algorithms/time_dependent.pyÚ qs€zcd_index..z&Not all nodes have a 'time' attribute.cs"h|] }ˆj|ˆˆkr|’qSr r©r Úi)r Ú target_daterr rÚ xs"zcd_index..zPAddition and comparison are not supported between 'time_delta' and 'time' types.cs0g|]‰t‡‡fdd„ˆˆDƒƒrdnd‘qS)c3s|] }|ˆˆvVqdSrr )r Új)r rr rr€ó€z&cd_index...éÿÿÿÿr)Úany)r ©r Únode)rrÚ €s0zcd_index..c3s$|] }ˆj| ¡ˆhVqdSr)ÚpredÚkeys)r Úsrr rrƒs€"rzThe cd index cannot be defined.Ncss|]}|VqdSrr )r Úbir r rr‰s€écsg|] }ˆj| ˆd¡‘qS)r)r Úgetr)r rr rrscss|] \}}||VqdSrr )r rÚwtr r rrŽr) ÚallÚnxZ NetworkXErrorr rÚlenÚunionÚroundÚsumÚzip) r rZ time_deltarrrÚbr Úweightsr )r rrrrrr s"h  ÿ" ")Ú__doc__Znetworkxr#Znetworkx.utilsrÚ__all__Z _dispatchablerr r r rÚs