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Code for Matching of Bipartite Graphs.ipynb
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{ | |
"cells": [ | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# Matching of Bipartite Graphs\n", | |
"## Create a bipartite graph" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 1, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"# imports\n", | |
"import networkx as nx\n", | |
"from networkx.algorithms import bipartite\n", | |
"\n", | |
"# Initialise graph\n", | |
"B = nx.Graph()\n", | |
"\n", | |
"# Add nodes with the node attribute \"bipartite\"\n", | |
"top_nodes = [1, 2, 3]\n", | |
"bottom_nodes = [\"A\", \"B\", \"C\"]\n", | |
"B.add_nodes_from(top_nodes, bipartite=0)\n", | |
"B.add_nodes_from(bottom_nodes, bipartite=1)\n", | |
"\n", | |
"# Add edges only between nodes of opposite node sets\n", | |
"B.add_edges_from([(1, \"A\"), (1, \"B\"), (2, \"B\"), (2, \"C\"), (3, \"A\"), (3, \"C\")])\n" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Maximum Cardinality Matching" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 2, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"{1: 'A', 2: 'D', 'A': 1, 'D': 2}\n" | |
] | |
} | |
], | |
"source": [ | |
"# Initialise graph\n", | |
"B = nx.Graph()\n", | |
"\n", | |
"# Add nodes with the node attribute \"bipartite\"\n", | |
"top_nodes = [1, 2]\n", | |
"bottom_nodes = [\"A\", \"B\", \"C\", \"D\"]\n", | |
"B.add_nodes_from(top_nodes, bipartite=0)\n", | |
"B.add_nodes_from(bottom_nodes, bipartite=1)\n", | |
"\n", | |
"# Add edges only between nodes of opposite node sets\n", | |
"B.add_edges_from([(1, \"A\"), (1, \"B\"), (1, \"C\"), (1, \"D\"), (2, \"A\"), (2, \"D\")])\n", | |
"\n", | |
"#Obtain the maximum cardinality matching\n", | |
"my_matching = bipartite.matching.hopcroft_karp_matching(B, top_nodes)\n", | |
"print(my_matching)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Minimum Weight Matching" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 3, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"{1: 'A', 2: 'B', 'A': 1, 'B': 2}\n" | |
] | |
} | |
], | |
"source": [ | |
"# Initialise the graph\n", | |
"B = nx.Graph()\n", | |
"\n", | |
"# Add nodes with the node attribute \"bipartite\"\n", | |
"top_nodes = [1, 2]\n", | |
"bottom_nodes = [\"A\", \"B\", \"C\", \"D\"]\n", | |
"B.add_nodes_from(top_nodes, bipartite=0)\n", | |
"B.add_nodes_from(bottom_nodes, bipartite=1)\n", | |
"\n", | |
"# Add edges with weights\n", | |
"B.add_edge(1, \"A\", weight = 1)\n", | |
"B.add_edge(1, \"B\", weight = 4)\n", | |
"B.add_edge(1, \"C\", weight = 2)\n", | |
"B.add_edge(1, \"D\", weight = 1)\n", | |
"B.add_edge(2, \"A\", weight = 3)\n", | |
"B.add_edge(2, \"B\", weight = 1)\n", | |
"B.add_edge(2, \"C\", weight = 2)\n", | |
"B.add_edge(2, \"D\", weight = 2)\n", | |
"\n", | |
"#Obtain the minimum weight full matching\n", | |
"my_matching = bipartite.matching.minimum_weight_full_matching(B, top_nodes, \"weight\")\n", | |
"print(my_matching)" | |
] | |
} | |
], | |
"metadata": { | |
"kernelspec": { | |
"display_name": "Python 3", | |
"language": "python", | |
"name": "python3" | |
}, | |
"language_info": { | |
"codemirror_mode": { | |
"name": "ipython", | |
"version": 3 | |
}, | |
"file_extension": ".py", | |
"mimetype": "text/x-python", | |
"name": "python", | |
"nbconvert_exporter": "python", | |
"pygments_lexer": "ipython3", | |
"version": "3.7.4" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 2 | |
} |
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