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annotate env/lib/python3.9/site-packages/networkx/algorithms/bipartite/__init__.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 r""" This module provides functions and operations for bipartite |
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2 graphs. Bipartite graphs `B = (U, V, E)` have two node sets `U,V` and edges in |
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3 `E` that only connect nodes from opposite sets. It is common in the literature |
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4 to use an spatial analogy referring to the two node sets as top and bottom nodes. |
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5 |
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6 The bipartite algorithms are not imported into the networkx namespace |
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7 at the top level so the easiest way to use them is with: |
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8 |
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9 >>> from networkx.algorithms import bipartite |
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10 |
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11 NetworkX does not have a custom bipartite graph class but the Graph() |
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12 or DiGraph() classes can be used to represent bipartite graphs. However, |
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13 you have to keep track of which set each node belongs to, and make |
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14 sure that there is no edge between nodes of the same set. The convention used |
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15 in NetworkX is to use a node attribute named `bipartite` with values 0 or 1 to |
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16 identify the sets each node belongs to. This convention is not enforced in |
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17 the source code of bipartite functions, it's only a recommendation. |
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18 |
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19 For example: |
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20 |
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21 >>> B = nx.Graph() |
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22 >>> # Add nodes with the node attribute "bipartite" |
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23 >>> B.add_nodes_from([1, 2, 3, 4], bipartite=0) |
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24 >>> B.add_nodes_from(["a", "b", "c"], bipartite=1) |
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25 >>> # Add edges only between nodes of opposite node sets |
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26 >>> B.add_edges_from([(1, "a"), (1, "b"), (2, "b"), (2, "c"), (3, "c"), (4, "a")]) |
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27 |
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28 Many algorithms of the bipartite module of NetworkX require, as an argument, a |
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29 container with all the nodes that belong to one set, in addition to the bipartite |
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30 graph `B`. The functions in the bipartite package do not check that the node set |
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31 is actually correct nor that the input graph is actually bipartite. |
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32 If `B` is connected, you can find the two node sets using a two-coloring |
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33 algorithm: |
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34 |
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35 >>> nx.is_connected(B) |
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36 True |
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37 >>> bottom_nodes, top_nodes = bipartite.sets(B) |
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38 |
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39 However, if the input graph is not connected, there are more than one possible |
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40 colorations. This is the reason why we require the user to pass a container |
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41 with all nodes of one bipartite node set as an argument to most bipartite |
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42 functions. In the face of ambiguity, we refuse the temptation to guess and |
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43 raise an :exc:`AmbiguousSolution <networkx.AmbiguousSolution>` |
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44 Exception if the input graph for |
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45 :func:`bipartite.sets <networkx.algorithms.bipartite.basic.sets>` |
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46 is disconnected. |
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47 |
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48 Using the `bipartite` node attribute, you can easily get the two node sets: |
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49 |
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50 >>> top_nodes = {n for n, d in B.nodes(data=True) if d["bipartite"] == 0} |
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51 >>> bottom_nodes = set(B) - top_nodes |
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52 |
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53 So you can easily use the bipartite algorithms that require, as an argument, a |
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54 container with all nodes that belong to one node set: |
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55 |
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56 >>> print(round(bipartite.density(B, bottom_nodes), 2)) |
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57 0.5 |
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58 >>> G = bipartite.projected_graph(B, top_nodes) |
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59 |
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60 All bipartite graph generators in NetworkX build bipartite graphs with the |
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61 `bipartite` node attribute. Thus, you can use the same approach: |
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62 |
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63 >>> RB = bipartite.random_graph(5, 7, 0.2) |
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64 >>> RB_top = {n for n, d in RB.nodes(data=True) if d["bipartite"] == 0} |
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65 >>> RB_bottom = set(RB) - RB_top |
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66 >>> list(RB_top) |
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67 [0, 1, 2, 3, 4] |
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68 >>> list(RB_bottom) |
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69 [5, 6, 7, 8, 9, 10, 11] |
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70 |
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71 For other bipartite graph generators see |
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72 :mod:`Generators <networkx.algorithms.bipartite.generators>`. |
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73 |
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74 """ |
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75 |
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76 from networkx.algorithms.bipartite.basic import * |
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77 from networkx.algorithms.bipartite.centrality import * |
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78 from networkx.algorithms.bipartite.cluster import * |
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79 from networkx.algorithms.bipartite.covering import * |
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80 from networkx.algorithms.bipartite.edgelist import * |
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81 from networkx.algorithms.bipartite.matching import * |
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82 from networkx.algorithms.bipartite.matrix import * |
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83 from networkx.algorithms.bipartite.projection import * |
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84 from networkx.algorithms.bipartite.redundancy import * |
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85 from networkx.algorithms.bipartite.spectral import * |
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86 from networkx.algorithms.bipartite.generators import * |