Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/covering.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 related to graph covers.""" |
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2 |
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3 import networkx as nx |
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4 from networkx.utils import not_implemented_for, arbitrary_element |
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5 from functools import partial |
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6 from itertools import chain |
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7 |
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8 |
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9 __all__ = ["min_edge_cover", "is_edge_cover"] |
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10 |
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11 |
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12 @not_implemented_for("directed") |
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13 @not_implemented_for("multigraph") |
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14 def min_edge_cover(G, matching_algorithm=None): |
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15 """Returns a set of edges which constitutes |
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16 the minimum edge cover of the graph. |
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17 |
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18 A smallest edge cover can be found in polynomial time by finding |
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19 a maximum matching and extending it greedily so that all nodes |
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20 are covered. |
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21 |
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22 Parameters |
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23 ---------- |
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24 G : NetworkX graph |
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25 An undirected bipartite graph. |
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26 |
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27 matching_algorithm : function |
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28 A function that returns a maximum cardinality matching in a |
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29 given bipartite graph. The function must take one input, the |
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30 graph ``G``, and return a dictionary mapping each node to its |
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31 mate. If not specified, |
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32 :func:`~networkx.algorithms.bipartite.matching.hopcroft_karp_matching` |
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33 will be used. Other possibilities include |
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34 :func:`~networkx.algorithms.bipartite.matching.eppstein_matching`, |
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35 or matching algorithms in the |
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36 :mod:`networkx.algorithms.matching` module. |
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37 |
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38 Returns |
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39 ------- |
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40 min_cover : set |
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41 |
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42 It contains all the edges of minimum edge cover |
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43 in form of tuples. It contains both the edges `(u, v)` and `(v, u)` |
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44 for given nodes `u` and `v` among the edges of minimum edge cover. |
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45 |
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46 Notes |
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47 ----- |
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48 An edge cover of a graph is a set of edges such that every node of |
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49 the graph is incident to at least one edge of the set. |
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50 The minimum edge cover is an edge covering of smallest cardinality. |
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51 |
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52 Due to its implementation, the worst-case running time of this algorithm |
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53 is bounded by the worst-case running time of the function |
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54 ``matching_algorithm``. |
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55 |
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56 Minimum edge cover for bipartite graph can also be found using the |
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57 function present in :mod:`networkx.algorithms.bipartite.covering` |
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58 """ |
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59 if nx.number_of_isolates(G) > 0: |
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60 # ``min_cover`` does not exist as there is an isolated node |
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61 raise nx.NetworkXException( |
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62 "Graph has a node with no edge incident on it, " "so no edge cover exists." |
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63 ) |
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64 if matching_algorithm is None: |
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65 matching_algorithm = partial(nx.max_weight_matching, maxcardinality=True) |
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66 maximum_matching = matching_algorithm(G) |
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67 # ``min_cover`` is superset of ``maximum_matching`` |
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68 try: |
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69 min_cover = set( |
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70 maximum_matching.items() |
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71 ) # bipartite matching case returns dict |
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72 except AttributeError: |
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73 min_cover = maximum_matching |
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74 # iterate for uncovered nodes |
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75 uncovered_nodes = set(G) - {v for u, v in min_cover} - {u for u, v in min_cover} |
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76 for v in uncovered_nodes: |
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77 # Since `v` is uncovered, each edge incident to `v` will join it |
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78 # with a covered node (otherwise, if there were an edge joining |
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79 # uncovered nodes `u` and `v`, the maximum matching algorithm |
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80 # would have found it), so we can choose an arbitrary edge |
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81 # incident to `v`. (This applies only in a simple graph, not a |
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82 # multigraph.) |
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83 u = arbitrary_element(G[v]) |
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84 min_cover.add((u, v)) |
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85 min_cover.add((v, u)) |
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86 return min_cover |
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87 |
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88 |
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89 @not_implemented_for("directed") |
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90 def is_edge_cover(G, cover): |
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91 """Decides whether a set of edges is a valid edge cover of the graph. |
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92 |
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93 Given a set of edges, whether it is an edge covering can |
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94 be decided if we just check whether all nodes of the graph |
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95 has an edge from the set, incident on it. |
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96 |
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97 Parameters |
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98 ---------- |
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99 G : NetworkX graph |
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100 An undirected bipartite graph. |
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101 |
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102 cover : set |
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103 Set of edges to be checked. |
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104 |
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105 Returns |
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106 ------- |
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107 bool |
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108 Whether the set of edges is a valid edge cover of the graph. |
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109 |
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110 Notes |
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111 ----- |
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112 An edge cover of a graph is a set of edges such that every node of |
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113 the graph is incident to at least one edge of the set. |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
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114 """ |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
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115 return set(G) <= set(chain.from_iterable(cover)) |