86 lines
3.1 KiB
Python
86 lines
3.1 KiB
Python
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"""Functions for computing the Voronoi cells of a graph."""
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import networkx as nx
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from networkx.utils import groups
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__all__ = ["voronoi_cells"]
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def voronoi_cells(G, center_nodes, weight="weight"):
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"""Returns the Voronoi cells centered at `center_nodes` with respect
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to the shortest-path distance metric.
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If *C* is a set of nodes in the graph and *c* is an element of *C*,
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the *Voronoi cell* centered at a node *c* is the set of all nodes
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*v* that are closer to *c* than to any other center node in *C* with
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respect to the shortest-path distance metric. [1]_
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For directed graphs, this will compute the "outward" Voronoi cells,
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as defined in [1]_, in which distance is measured from the center
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nodes to the target node. For the "inward" Voronoi cells, use the
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:meth:`DiGraph.reverse` method to reverse the orientation of the
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edges before invoking this function on the directed graph.
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Parameters
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----------
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G : NetworkX graph
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center_nodes : set
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A nonempty set of nodes in the graph `G` that represent the
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center of the Voronoi cells.
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weight : string or function
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The edge attribute (or an arbitrary function) representing the
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weight of an edge. This keyword argument is as described in the
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documentation for :func:`~networkx.multi_source_dijkstra_path`,
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for example.
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Returns
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-------
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dictionary
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A mapping from center node to set of all nodes in the graph
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closer to that center node than to any other center node. The
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keys of the dictionary are the element of `center_nodes`, and
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the values of the dictionary form a partition of the nodes of
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`G`.
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Examples
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--------
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To get only the partition of the graph induced by the Voronoi cells,
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take the collection of all values in the returned dictionary::
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>>> G = nx.path_graph(6)
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>>> center_nodes = {0, 3}
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>>> cells = nx.voronoi_cells(G, center_nodes)
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>>> partition = set(map(frozenset, cells.values()))
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>>> sorted(map(sorted, partition))
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[[0, 1], [2, 3, 4, 5]]
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Raises
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------
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ValueError
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If `center_nodes` is empty.
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References
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----------
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.. [1] Erwig, Martin. (2000),
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"The graph Voronoi diagram with applications."
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*Networks*, 36: 156--163.
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<dx.doi.org/10.1002/1097-0037(200010)36:3<156::AID-NET2>3.0.CO;2-L>
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"""
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# Determine the shortest paths from any one of the center nodes to
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# every node in the graph.
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#
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# This raises `ValueError` if `center_nodes` is an empty set.
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paths = nx.multi_source_dijkstra_path(G, center_nodes, weight=weight)
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# Determine the center node from which the shortest path originates.
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nearest = {v: p[0] for v, p in paths.items()}
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# Get the mapping from center node to all nodes closer to it than to
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# any other center node.
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cells = groups(nearest)
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# We collect all unreachable nodes under a special key, if there are any.
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unreachable = set(G) - set(nearest)
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if unreachable:
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cells["unreachable"] = unreachable
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return cells
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