Shortest_path.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d9a88783-aa1a-4699-a9bd-8681d5bcee41",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: gurobipy in /home/therring/.local/lib/python3.9/site-packages (9.5.1)\n",
      "Requirement already satisfied: networkx in /home/therring/.local/lib/python3.9/site-packages (2.7.1)\n",
      "Requirement already satisfied: pydot in /home/therring/.local/lib/python3.9/site-packages (1.4.2)\n",
      "Requirement already satisfied: pyparsing>=2.1.4 in /usr/lib/python3/dist-packages (from pydot) (2.4.7)\n",
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "%pip install gurobipy networkx pydot\n",
    "#sudo apt install graphviz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "dbf0cbca-a10d-4d10-a3a1-620fecd377ef",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pydot as pd\n",
    "from IPython.display import SVG, display\n",
    "from costgraph.Functions import *\n",
    "from costgraph.Models import *\n",
    "from costgraph.Graph import *\n",
    "from costgraph.Viz import *\n",
    "from costgraph.Constants import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "fbb29878-9867-4390-9fd7-3d836cf0d87b",
   "metadata": {},
   "outputs": [],
   "source": [
    "costly_edge = EdgeCostLinear(6,2,3,10)\n",
    "cheap_edge = EdgeCostExponential(10,6,1,8,0.7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "93ead0ff-b18b-43bd-9291-9dccb71878ef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "graphEdgeFunc(\"Cheap Edge (a-c)\", cheap_edge)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ae35c1a0-7c6c-411f-a64b-b50d361662ab",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "graphEdgeFunc(\"Costly Edge (a-b, b-c)\", costly_edge)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6245b18d-505c-4dd1-a402-9c54c37dcdd7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x180 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "showEdgeFuncImg(cheap_edge, 6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b38582b7-f907-485d-bd0b-70f1cafebae0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G = CostFuncGraph()\n",
    "G.add_edge(\"a\", \"b\", costly_edge)\n",
    "G.add_edge(\"b\", \"c\", costly_edge)\n",
    "G.add_edge(\"a\", \"c\", cheap_edge)\n",
    "\n",
    "nx.draw(G, with_labels=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "67e34564-101e-4a9a-a1c2-6006fa1a64c8",
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\" MODEL PARAMETERS \"\"\"\n",
    "\n",
    "start_node = 'a'\n",
    "end_node = 'c'\n",
    "\n",
    "# Budget for planning problem\n",
    "#B = 22\n",
    "#B = 16.3\n",
    "B = 16.8\n",
    "# Number of points in piecewise approximation of edge cost functions\n",
    "n = 300"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "a2afd663-da51-4814-b895-45d11d0436d2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Set parameter Username\n",
      "Academic license - for non-commercial use only - expires 2022-05-14\n",
      "a -> b: b=8.41204 c=2.90741\n",
      "b -> c: b=8.38796 c=2.92117\n",
      "Total budget used: 16.8\n",
      "Total cost for path: 5.82857\n"
     ]
    }
   ],
   "source": [
    "model = Model(G, start_node, end_node, B, n)\n",
    "s_path = model.solve(print_path=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "6634de09-4dd4-48c8-8b92-e503e0824123",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cheapest long path (a->b, b->c): 5.828571428571429\n",
      "Cheapest short path (a->c): 6.000062916277819\n"
     ]
    }
   ],
   "source": [
    "cheapest_long = G.edges[('a','b')]['f'].f(B/2) + G.edges[('b','c')]['f'].f(B/2)\n",
    "print(f\"Cheapest long path (a->b, b->c): {cheapest_long}\")\n",
    "cheapest_short = G.edges[('a','c')]['f'].f(B)\n",
    "print(f\"Cheapest short path (a->c): {cheapest_short}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "dff17391-3cde-43d4-b7ff-201d0f0118a9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x180 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x180 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "saveGraphImgs(G,s_path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "76a05f80-ce3f-42b1-a14f-72937d28cae1",
   "metadata": {},
   "outputs": [],
   "source": [
    "G.label_path(s_path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "79a64c04-9941-4c76-bf56-de49d8326a0c",
   "metadata": {},
   "outputs": [],
   "source": [
    "G_dot = G.toDot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "9eae0746-ffe0-4afa-8fa6-b6b6b5848efd",
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "add_edge() got an unexpected keyword argument 'label'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "Input \u001b[0;32mIn [25]\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m u,v \u001b[38;5;129;01min\u001b[39;00m G\u001b[38;5;241m.\u001b[39medges():\n\u001b[1;32m      2\u001b[0m     \u001b[38;5;66;03m#G_dot.get_edge((u,v))[0].set_label(\u001b[39;00m\n\u001b[0;32m----> 3\u001b[0m     \u001b[43mG\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43madd_edge\u001b[49m\u001b[43m(\u001b[49m\u001b[43mu\u001b[49m\u001b[43m,\u001b[49m\u001b[43mv\u001b[49m\u001b[43m,\u001b[49m\u001b[43mlabel\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\n\u001b[1;32m      4\u001b[0m \u001b[43m        \u001b[49m\u001b[38;5;124;43mf\u001b[39;49m\u001b[38;5;124;43m\"\"\"\u001b[39;49m\u001b[38;5;124;43m<<TABLE \u001b[39;49m\n\u001b[1;32m      5\u001b[0m \u001b[38;5;124;43m        BORDER=\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43m0\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\n\u001b[1;32m      6\u001b[0m \u001b[38;5;124;43m        >\u001b[39;49m\n\u001b[1;32m      7\u001b[0m \u001b[38;5;124;43m        <TR><TD><IMG SRC=\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43m/home/therring/Workspace/costgraph/imgs/edgecosts/\u001b[39;49m\u001b[38;5;132;43;01m{\u001b[39;49;00m\u001b[43mu\u001b[49m\u001b[38;5;132;43;01m}\u001b[39;49;00m\u001b[38;5;124;43m-\u001b[39;49m\u001b[38;5;132;43;01m{\u001b[39;49;00m\u001b[43mv\u001b[49m\u001b[38;5;132;43;01m}\u001b[39;49;00m\u001b[38;5;124;43m.png\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43m/></TD></TR>\u001b[39;49m\n\u001b[1;32m      8\u001b[0m \u001b[38;5;124;43m        </TABLE>>\u001b[39;49m\u001b[38;5;124;43m\"\"\"\u001b[39;49m\u001b[43m)\u001b[49m\n",
      "\u001b[0;31mTypeError\u001b[0m: add_edge() got an unexpected keyword argument 'label'"
     ]
    }
   ],
   "source": [
    "for u,v in G.edges():\n",
    "    #G_dot.get_edge((u,v))[0].set_label(\n",
    "    G.add_edge(u,v,label=\n",
    "        f\"\"\"<<TABLE \n",
    "        BORDER=\"0\"\n",
    "        >\n",
    "        <TR><TD><IMG SRC=\"/home/therring/Workspace/costgraph/imgs/edgecosts/{u}-{v}.png\"/></TD></TR>\n",
    "        </TABLE>>\"\"\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "62e90910-1d85-45be-990e-d876d9f6b3c1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\"dot\" with args ['-Tsvg', '/tmp/tmpjsst2prp'] returned code: 1\n",
      "\n",
      "stdout, stderr:\n",
      " b'<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\\n \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\\n<!-- Generated by graphviz version 2.43.0 (0)\\n -->\\n<!-- Title: %3 Pages: 1 -->\\n<svg width=\"103pt\" height=\"204pt\"\\n viewBox=\"0.00 0.00 103.00 204.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\\n<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 200)\">\\n<title>%3</title>\\n<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-200 99,-200 99,4 -4,4\"/>\\n<!-- a -->\\n<g id=\"node1\" class=\"node\">\\n<title>a</title>\\n<ellipse fill=\"none\" stroke=\"black\" cx=\"68\" cy=\"-178\" rx=\"27\" ry=\"18\"/>\\n<text text-anchor=\"middle\" x=\"68\" y=\"-174.3\" font-family=\"Times,serif\" font-size=\"14.00\">a</text>\\n</g>\\n<!-- b -->\\n<g id=\"node2\" class=\"node\">\\n<title>b</title>\\n<ellipse fill=\"none\" stroke=\"black\" cx=\"27\" cy=\"-98\" rx=\"27\" ry=\"18\"/>\\n<text text-anchor=\"middle\" x=\"27\" y=\"-94.3\" font-family=\"Times,serif\" font-size=\"14.00\">b</text>\\n</g>\\n<!-- a&#45;&gt;b -->\\n<g id=\"edge1\" class=\"edge\">\\n<title>a&#45;&gt;b</title>\\n<path fill=\"none\" stroke=\"black\" d=\"M59.5,-160.84C53.95,-150.28 46.59,-136.26 40.27,-124.25\"/>\\n<polygon fill=\"black\" stroke=\"black\" points=\"43.24,-122.36 35.48,-115.14 37.04,-125.62 43.24,-122.36\"/>\\n</g>\\n<!-- c -->\\n<g id=\"node3\" class=\"node\">\\n<title>c</title>\\n<ellipse fill=\"none\" stroke=\"black\" cx=\"54\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\\n<text text-anchor=\"middle\" x=\"54\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">c</text>\\n</g>\\n<!-- a&#45;&gt;c -->\\n<g id=\"edge2\" class=\"edge\">\\n<title>a&#45;&gt;c</title>\\n<path fill=\"none\" stroke=\"black\" d=\"M67.61,-159.79C67.05,-140.37 65.77,-107.85 63,-80 61.89,-68.81 60.18,-56.54 58.54,-45.96\"/>\\n<polygon fill=\"black\" stroke=\"black\" points=\"61.99,-45.36 56.96,-36.04 55.08,-46.46 61.99,-45.36\"/>\\n</g>\\n<!-- b&#45;&gt;c -->\\n<g id=\"edge3\" class=\"edge\">\\n<title>b&#45;&gt;c</title>\\n<path fill=\"none\" stroke=\"black\" d=\"M32.86,-80.08C36.39,-69.89 40.95,-56.7 44.93,-45.19\"/>\\n<polygon fill=\"black\" stroke=\"black\" points=\"48.28,-46.22 48.25,-35.62 41.67,-43.93 48.28,-46.22\"/>\\n</g>\\n</g>\\n</svg>\\n'\n",
      "b'Warning: No such file or directory while opening /home/therring/Workspace/costgraph/imgs/edgecosts/a-b.svg\\nError: No or improper image file=\"/home/therring/Workspace/costgraph/imgs/edgecosts/a-b.svg\"\\nin label of edge a -> b\\nWarning: No such file or directory while opening /home/therring/Workspace/costgraph/imgs/edgecosts/b-c.svg\\nError: No or improper image file=\"/home/therring/Workspace/costgraph/imgs/edgecosts/b-c.svg\"\\nin label of edge b -> c\\n'\n",
      "\n"
     ]
    },
    {
     "ename": "AssertionError",
     "evalue": "\"dot\" with args ['-Tsvg', '/tmp/tmpjsst2prp'] returned code: 1",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAssertionError\u001b[0m                            Traceback (most recent call last)",
      "Input \u001b[0;32mIn [12]\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0m img \u001b[38;5;241m=\u001b[39m \u001b[43mG_dot\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mcreate_svg\u001b[49m\u001b[43m(\u001b[49m\u001b[43mprog\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mdot\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m      2\u001b[0m display(SVG(img))\n",
      "File \u001b[0;32m~/.local/lib/python3.9/site-packages/pydot.py:1733\u001b[0m, in \u001b[0;36mDot.__init__.<locals>.new_method\u001b[0;34m(f, prog, encoding)\u001b[0m\n\u001b[1;32m   1729\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mnew_method\u001b[39m(\n\u001b[1;32m   1730\u001b[0m         f\u001b[38;5;241m=\u001b[39mfrmt, prog\u001b[38;5;241m=\u001b[39m\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mprog,\n\u001b[1;32m   1731\u001b[0m         encoding\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m):\n\u001b[1;32m   1732\u001b[0m     \u001b[38;5;124;03m\"\"\"Refer to docstring of method `create`.\"\"\"\u001b[39;00m\n\u001b[0;32m-> 1733\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mcreate\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m   1734\u001b[0m \u001b[43m        \u001b[49m\u001b[38;5;28;43mformat\u001b[39;49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mf\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mprog\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mprog\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mencoding\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mencoding\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/.local/lib/python3.9/site-packages/pydot.py:1956\u001b[0m, in \u001b[0;36mDot.create\u001b[0;34m(self, prog, format, encoding)\u001b[0m\n\u001b[1;32m   1944\u001b[0m     message \u001b[38;5;241m=\u001b[39m (\n\u001b[1;32m   1945\u001b[0m         \u001b[38;5;124m'\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;132;01m{prog}\u001b[39;00m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m with args \u001b[39m\u001b[38;5;132;01m{arguments}\u001b[39;00m\u001b[38;5;124m returned code: \u001b[39m\u001b[38;5;132;01m{code}\u001b[39;00m\u001b[38;5;130;01m\\n\u001b[39;00m\u001b[38;5;130;01m\\n\u001b[39;00m\u001b[38;5;124m'\u001b[39m\n\u001b[1;32m   1946\u001b[0m         \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mstdout, stderr:\u001b[39m\u001b[38;5;130;01m\\n\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;132;01m{out}\u001b[39;00m\u001b[38;5;130;01m\\n\u001b[39;00m\u001b[38;5;132;01m{err}\u001b[39;00m\u001b[38;5;130;01m\\n\u001b[39;00m\u001b[38;5;124m'\u001b[39m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m   1952\u001b[0m         err\u001b[38;5;241m=\u001b[39mstderr_data,\n\u001b[1;32m   1953\u001b[0m     )\n\u001b[1;32m   1954\u001b[0m     \u001b[38;5;28mprint\u001b[39m(message)\n\u001b[0;32m-> 1956\u001b[0m \u001b[38;5;28;01massert\u001b[39;00m process\u001b[38;5;241m.\u001b[39mreturncode \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m0\u001b[39m, (\n\u001b[1;32m   1957\u001b[0m         \u001b[38;5;124m'\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;132;01m{prog}\u001b[39;00m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m with args \u001b[39m\u001b[38;5;132;01m{arguments}\u001b[39;00m\u001b[38;5;124m returned code: \u001b[39m\u001b[38;5;132;01m{code}\u001b[39;00m\u001b[38;5;124m'\u001b[39m\u001b[38;5;241m.\u001b[39mformat(\n\u001b[1;32m   1958\u001b[0m             prog\u001b[38;5;241m=\u001b[39mprog,\n\u001b[1;32m   1959\u001b[0m             arguments\u001b[38;5;241m=\u001b[39marguments,\n\u001b[1;32m   1960\u001b[0m             code\u001b[38;5;241m=\u001b[39mprocess\u001b[38;5;241m.\u001b[39mreturncode,\n\u001b[1;32m   1961\u001b[0m         )\n\u001b[1;32m   1962\u001b[0m     )\n\u001b[1;32m   1964\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m stdout_data\n",
      "\u001b[0;31mAssertionError\u001b[0m: \"dot\" with args ['-Tsvg', '/tmp/tmpjsst2prp'] returned code: 1"
     ]
    }
   ],
   "source": [
    "img = G_dot.create_svg(prog='dot')\n",
    "display(SVG(img))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "bb32719a-d6e9-4b98-b4af-bc906202ba0a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G_dot.write(\"triangular.dot\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "b7ccdc1b-abd4-4121-a229-e0997b142d54",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "strict digraph  {\n",
      "a;\n",
      "b;\n",
      "c;\n",
      "a -> b  [b=\"8.412040133779264\", c=\"2.907405637840421\", f=<costgraph.Functions.EdgeCostLinear object at 0x7f8b4d7aa610>, label=<<TABLE \n",
      "            BORDER=\"0\"\n",
      "            >\n",
      "            <TR><TD><IMG SRC=\"{}\"/></TD></TR>\n",
      "            </TABLE>>];\n",
      "a -> c  [f=<costgraph.Functions.EdgeCostExponential object at 0x7f8b4c735d30>];\n",
      "b -> c  [b=\"8.387959866220736\", c=\"2.921165790731008\", f=<costgraph.Functions.EdgeCostLinear object at 0x7f8b4d7aa610>, label=<<TABLE \n",
      "            BORDER=\"0\"\n",
      "            >\n",
      "            <TR><TD><IMG SRC=\"{}\"/></TD></TR>\n",
      "            </TABLE>>];\n",
      "}\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(G_dot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "990111e8-ab07-44bc-830c-a37491e402f2",
   "metadata": {},
   "outputs": [],
   "source": [
    "#"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
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