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+"""
+Time Series Graphs
+"""
+
+import itertools
+
+import networkx as nx
+
+__all__ = ["visibility_graph"]
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+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