Code for Matching of Bipartite Graphs.ipynb

Code for Matching of Bipartite Graphs.ipynb

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   "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)"
   ]
  }
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