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| """ | |
| Time Series Graphs | |
| """ | |
| import itertools | |
| import networkx as nx | |
| __all__ = ["visibility_graph"] | |
| def visibility_graph(series): | |
| """ | |
| Return a Visibility Graph of an input Time Series. | |
| A visibility graph converts a time series into a graph. The constructed graph | |
| uses integer nodes to indicate which event in the series the node represents. | |
| Edges are formed as follows: consider a bar plot of the series and view that | |
| as a side view of a landscape with a node at the top of each bar. An edge | |
| means that the nodes can be connected by a straight "line-of-sight" without | |
| being obscured by any bars between the nodes. | |
| The resulting graph inherits several properties of the series in its structure. | |
| Thereby, periodic series convert into regular graphs, random series convert | |
| into random graphs, and fractal series convert into scale-free networks [1]_. | |
| Parameters | |
| ---------- | |
| series : Sequence[Number] | |
| A Time Series sequence (iterable and sliceable) of numeric values | |
| representing times. | |
| Returns | |
| ------- | |
| NetworkX Graph | |
| The Visibility Graph of the input series | |
| Examples | |
| -------- | |
| >>> series_list = [range(10), [2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3]] | |
| >>> for s in series_list: | |
| ... g = nx.visibility_graph(s) | |
| ... print(g) | |
| Graph with 10 nodes and 9 edges | |
| Graph with 12 nodes and 18 edges | |
| References | |
| ---------- | |
| .. [1] Lacasa, Lucas, Bartolo Luque, Fernando Ballesteros, Jordi Luque, and Juan Carlos Nuno. | |
| "From time series to complex networks: The visibility graph." Proceedings of the | |
| National Academy of Sciences 105, no. 13 (2008): 4972-4975. | |
| https://www.pnas.org/doi/10.1073/pnas.0709247105 | |
| """ | |
| # Sequential values are always connected | |
| G = nx.path_graph(len(series)) | |
| nx.set_node_attributes(G, dict(enumerate(series)), "value") | |
| # Check all combinations of nodes n series | |
| for (n1, t1), (n2, t2) in itertools.combinations(enumerate(series), 2): | |
| # check if any value between obstructs line of sight | |
| slope = (t2 - t1) / (n2 - n1) | |
| offset = t2 - slope * n2 | |
| obstructed = any( | |
| t >= slope * n + offset | |
| for n, t in enumerate(series[n1 + 1 : n2], start=n1 + 1) | |
| ) | |
| if not obstructed: | |
| G.add_edge(n1, n2) | |
| return G | |