Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/voronoi.py @ 0:4f3585e2f14b draft default tip
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author | shellac |
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date | Mon, 22 Mar 2021 18:12:50 +0000 |
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1 """Functions for computing the Voronoi cells of a graph.""" |
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2 import networkx as nx |
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3 from networkx.utils import groups |
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4 |
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5 __all__ = ["voronoi_cells"] |
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6 |
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7 |
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8 def voronoi_cells(G, center_nodes, weight="weight"): |
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9 """Returns the Voronoi cells centered at `center_nodes` with respect |
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10 to the shortest-path distance metric. |
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11 |
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12 If *C* is a set of nodes in the graph and *c* is an element of *C*, |
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13 the *Voronoi cell* centered at a node *c* is the set of all nodes |
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14 *v* that are closer to *c* than to any other center node in *C* with |
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15 respect to the shortest-path distance metric. [1]_ |
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16 |
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17 For directed graphs, this will compute the "outward" Voronoi cells, |
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18 as defined in [1]_, in which distance is measured from the center |
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19 nodes to the target node. For the "inward" Voronoi cells, use the |
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20 :meth:`DiGraph.reverse` method to reverse the orientation of the |
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21 edges before invoking this function on the directed graph. |
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22 |
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23 Parameters |
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24 ---------- |
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25 G : NetworkX graph |
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26 |
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27 center_nodes : set |
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28 A nonempty set of nodes in the graph `G` that represent the |
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29 center of the Voronoi cells. |
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30 |
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31 weight : string or function |
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32 The edge attribute (or an arbitrary function) representing the |
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33 weight of an edge. This keyword argument is as described in the |
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34 documentation for :func:`~networkx.multi_source_dijkstra_path`, |
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35 for example. |
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36 |
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37 Returns |
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38 ------- |
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39 dictionary |
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40 A mapping from center node to set of all nodes in the graph |
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41 closer to that center node than to any other center node. The |
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42 keys of the dictionary are the element of `center_nodes`, and |
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43 the values of the dictionary form a partition of the nodes of |
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44 `G`. |
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45 |
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46 Examples |
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47 -------- |
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48 To get only the partition of the graph induced by the Voronoi cells, |
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49 take the collection of all values in the returned dictionary:: |
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50 |
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51 >>> G = nx.path_graph(6) |
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52 >>> center_nodes = {0, 3} |
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53 >>> cells = nx.voronoi_cells(G, center_nodes) |
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54 >>> partition = set(map(frozenset, cells.values())) |
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55 >>> sorted(map(sorted, partition)) |
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56 [[0, 1], [2, 3, 4, 5]] |
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57 |
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58 Raises |
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59 ------ |
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60 ValueError |
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61 If `center_nodes` is empty. |
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62 |
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63 References |
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64 ---------- |
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65 .. [1] Erwig, Martin. (2000), |
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66 "The graph Voronoi diagram with applications." |
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67 *Networks*, 36: 156--163. |
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68 <dx.doi.org/10.1002/1097-0037(200010)36:3<156::AID-NET2>3.0.CO;2-L> |
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69 |
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70 """ |
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71 # Determine the shortest paths from any one of the center nodes to |
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72 # every node in the graph. |
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73 # |
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74 # This raises `ValueError` if `center_nodes` is an empty set. |
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75 paths = nx.multi_source_dijkstra_path(G, center_nodes, weight=weight) |
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76 # Determine the center node from which the shortest path originates. |
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77 nearest = {v: p[0] for v, p in paths.items()} |
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78 # Get the mapping from center node to all nodes closer to it than to |
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79 # any other center node. |
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80 cells = groups(nearest) |
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81 # We collect all unreachable nodes under a special key, if there are any. |
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82 unreachable = set(G) - set(nearest) |
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83 if unreachable: |
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84 cells["unreachable"] = unreachable |
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85 return cells |