Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/connectivity/utils.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 """ |
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2 Utilities for connectivity package |
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3 """ |
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4 import networkx as nx |
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5 |
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6 __all__ = ["build_auxiliary_node_connectivity", "build_auxiliary_edge_connectivity"] |
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7 |
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8 |
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9 def build_auxiliary_node_connectivity(G): |
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10 r"""Creates a directed graph D from an undirected graph G to compute flow |
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11 based node connectivity. |
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12 |
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13 For an undirected graph G having `n` nodes and `m` edges we derive a |
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14 directed graph D with `2n` nodes and `2m+n` arcs by replacing each |
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15 original node `v` with two nodes `vA`, `vB` linked by an (internal) |
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16 arc in D. Then for each edge (`u`, `v`) in G we add two arcs (`uB`, `vA`) |
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17 and (`vB`, `uA`) in D. Finally we set the attribute capacity = 1 for each |
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18 arc in D [1]_. |
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19 |
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20 For a directed graph having `n` nodes and `m` arcs we derive a |
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21 directed graph D with `2n` nodes and `m+n` arcs by replacing each |
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22 original node `v` with two nodes `vA`, `vB` linked by an (internal) |
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23 arc (`vA`, `vB`) in D. Then for each arc (`u`, `v`) in G we add one |
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24 arc (`uB`, `vA`) in D. Finally we set the attribute capacity = 1 for |
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25 each arc in D. |
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26 |
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27 A dictionary with a mapping between nodes in the original graph and the |
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28 auxiliary digraph is stored as a graph attribute: H.graph['mapping']. |
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29 |
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30 References |
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31 ---------- |
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32 .. [1] Kammer, Frank and Hanjo Taubig. Graph Connectivity. in Brandes and |
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33 Erlebach, 'Network Analysis: Methodological Foundations', Lecture |
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34 Notes in Computer Science, Volume 3418, Springer-Verlag, 2005. |
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35 http://www.informatik.uni-augsburg.de/thi/personen/kammer/Graph_Connectivity.pdf |
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36 |
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37 """ |
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38 directed = G.is_directed() |
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39 |
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40 mapping = {} |
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41 H = nx.DiGraph() |
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42 |
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43 for i, node in enumerate(G): |
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44 mapping[node] = i |
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45 H.add_node(f"{i}A", id=node) |
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46 H.add_node(f"{i}B", id=node) |
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47 H.add_edge(f"{i}A", f"{i}B", capacity=1) |
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48 |
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49 edges = [] |
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50 for (source, target) in G.edges(): |
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51 edges.append((f"{mapping[source]}B", f"{mapping[target]}A")) |
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52 if not directed: |
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53 edges.append((f"{mapping[target]}B", f"{mapping[source]}A")) |
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54 H.add_edges_from(edges, capacity=1) |
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55 |
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56 # Store mapping as graph attribute |
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57 H.graph["mapping"] = mapping |
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58 return H |
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59 |
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60 |
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61 def build_auxiliary_edge_connectivity(G): |
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62 """Auxiliary digraph for computing flow based edge connectivity |
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63 |
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64 If the input graph is undirected, we replace each edge (`u`,`v`) with |
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65 two reciprocal arcs (`u`, `v`) and (`v`, `u`) and then we set the attribute |
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66 'capacity' for each arc to 1. If the input graph is directed we simply |
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67 add the 'capacity' attribute. Part of algorithm 1 in [1]_ . |
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68 |
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69 References |
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70 ---------- |
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71 .. [1] Abdol-Hossein Esfahanian. Connectivity Algorithms. (this is a |
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72 chapter, look for the reference of the book). |
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73 http://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf |
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74 """ |
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75 if G.is_directed(): |
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76 H = nx.DiGraph() |
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77 H.add_nodes_from(G.nodes()) |
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78 H.add_edges_from(G.edges(), capacity=1) |
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79 return H |
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80 else: |
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81 H = nx.DiGraph() |
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82 H.add_nodes_from(G.nodes()) |
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83 for (source, target) in G.edges(): |
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84 H.add_edges_from([(source, target), (target, source)], capacity=1) |
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85 return H |