{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Diskrete Mathematik\n",
    "\n",
    "Python bietet diverse Funktionen, um grundlegende Konzepte aus der Kombinatorik umzusetzen.\n",
    "Zum Beispiel lassen sich alle Kombinationen von zwei oder mehr Mengen mittels der Funktion `product` bilden, oder geordnete Auswahlen aus einer Liste mit oder ohne zurücklegen treffen.\n",
    "\n",
    "Dokumentation: [itertools](https://docs.python.org/2/library/itertools.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Für die folgenden Beispiele definieren wir uns die folgenden zwei diskrete Mengen (eine Liste ist OK)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "animals = [\"cat\", \"dog\", \"fish\"]\n",
    "owners = [\"susi\", \"tim\", \"franziska\", \"henry\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Produktbildung\n",
    "\n",
    "Alle Kombinationen durchprobieren"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cat   belongs to susi      \n",
      "cat   belongs to tim       \n",
      "cat   belongs to franziska \n",
      "cat   belongs to henry     \n",
      "dog   belongs to susi      \n",
      "dog   belongs to tim       \n",
      "dog   belongs to franziska \n",
      "dog   belongs to henry     \n",
      "fish  belongs to susi      \n",
      "fish  belongs to tim       \n",
      "fish  belongs to franziska \n",
      "fish  belongs to henry     \n"
     ]
    }
   ],
   "source": [
    "from itertools import product\n",
    "for animal, owner in product(animals, owners):\n",
    "    print(\"%-5s belongs to %-10s\" % (animal, owner))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Kombinationen aus einer Menge ziehen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "susi      \n",
      "tim       \n",
      "franziska \n",
      "henry     \n"
     ]
    }
   ],
   "source": [
    "# Ziehe 1 ...\n",
    "from itertools import combinations\n",
    "for owner1 in combinations(owners, 1):\n",
    "    print(\"%-10s\" % (owner1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "susi       tim       \n",
      "susi       franziska \n",
      "susi       henry     \n",
      "tim        franziska \n",
      "tim        henry     \n",
      "franziska  henry     \n"
     ]
    }
   ],
   "source": [
    "# ... ziehe 2 ...\n",
    "from itertools import combinations\n",
    "for owner1, owner2 in combinations(owners, 2):\n",
    "    print(\"%-10s %-10s\" % (owner1, owner2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "susi       tim        franziska \n",
      "susi       tim        henry     \n",
      "susi       franziska  henry     \n",
      "tim        franziska  henry     \n"
     ]
    }
   ],
   "source": [
    "# ... oder 3 ....\n",
    "from itertools import combinations\n",
    "for owner1, owner2, owner3 in combinations(owners, 3):\n",
    "    print(\"%-10s %-10s %-10s\" % (owner1, owner2, owner3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "susi       tim        franziska  henry     \n"
     ]
    }
   ],
   "source": [
    "# ... oder gar 4!\n",
    "from itertools import combinations\n",
    "for owner1, owner2, owner3, owner4 in combinations(owners, 4):\n",
    "    print(\"%-10s %-10s %-10s %-10s\" % (owner1, owner2, owner3, owner4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Kombinationen mit Zurücklegen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "susi       susi      \n",
      "susi       tim       \n",
      "susi       franziska \n",
      "susi       henry     \n",
      "tim        tim       \n",
      "tim        franziska \n",
      "tim        henry     \n",
      "franziska  franziska \n",
      "franziska  henry     \n",
      "henry      henry     \n"
     ]
    }
   ],
   "source": [
    "from itertools import combinations_with_replacement\n",
    "for owner1, owner2 in combinations_with_replacement(owners, 2):\n",
    "    print(\"%-10s %-10s\" % (owner1, owner2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Permutationen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "susi       tim       \n",
      "susi       franziska \n",
      "susi       henry     \n",
      "tim        susi      \n",
      "tim        franziska \n",
      "tim        henry     \n",
      "franziska  susi      \n",
      "franziska  tim       \n",
      "franziska  henry     \n",
      "henry      susi      \n",
      "henry      tim       \n",
      "henry      franziska \n"
     ]
    }
   ],
   "source": [
    "from itertools import permutations\n",
    "for owner1, owner2 in permutations(owners, 2):\n",
    "    print(\"%-10s %-10s\" % (owner1, owner2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "susi       tim        franziska \n",
      "susi       tim        henry     \n",
      "susi       franziska  tim       \n",
      "susi       franziska  henry     \n",
      "susi       henry      tim       \n",
      "susi       henry      franziska \n",
      "tim        susi       franziska \n",
      "tim        susi       henry     \n",
      "tim        franziska  susi      \n",
      "tim        franziska  henry     \n",
      "tim        henry      susi      \n",
      "tim        henry      franziska \n",
      "franziska  susi       tim       \n",
      "franziska  susi       henry     \n",
      "franziska  tim        susi      \n",
      "franziska  tim        henry     \n",
      "franziska  henry      susi      \n",
      "franziska  henry      tim       \n",
      "henry      susi       tim       \n",
      "henry      susi       franziska \n",
      "henry      tim        susi      \n",
      "henry      tim        franziska \n",
      "henry      franziska  susi      \n",
      "henry      franziska  tim       \n"
     ]
    }
   ],
   "source": [
    "from itertools import permutations\n",
    "for owner1, owner2, owner3 in permutations(owners, 3):\n",
    "    print(\"%-10s %-10s %-10s\" % (owner1, owner2, owner3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Graphen\n",
    "\n",
    "[NetworkX](https://networkx.github.io/) ist eine der am weitesten verbreiteten Python-Bibliotheken für Graphentheorie\n",
    "mit einer [Menge von Algorithmen](http://networkx.github.io/documentation/latest/reference/algorithms.html).\n",
    "\n",
    "\n",
    "[NetworkX Dokumentation](http://networkx.github.io/documentation/networkx-1.9.1/)\n",
    "\n",
    "(Eine andere Pythonbibliothek wäre [SageMath / Graph Theory](http://doc.sagemath.org/html/en/reference/graphs/index.html))\n",
    "\n",
    "Ein Graph ist eine Menge von Knoten und Kanten (Vertices and Edges),\n",
    "wobei die Kanten für Verbindungen zwischen den Knoten stehen.\n",
    "Es gibt ungerichtete und gerichtete Verbindungen -- letzteres ist dann ein \"gerichteter Graph\".\n",
    "Eine Implementierung im Computer besteht nun darin,\n",
    "in einer Datenstruktur diese Kanten und Knoten effizient zu verwalten\n",
    "und dann darauf aufbauend Algorithmen aus der Graphentheorie anzuwenden.\n",
    "\n",
    "Bemerkung: Falls die Bibliothek `networkx` nicht installiert sein sollte, so kann man dies entweder in der Kommandozeile oder in Canopy unter Tools → Canopy Terminal mittels\n",
    "\n",
    "    pip install networkx\n",
    "    \n",
    "nachholen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'1.11'"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import networkx as nx\n",
    "%matplotlib inline\n",
    "nx.__version__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hier wird ein einfacher Graph instanziert. Die Knoten sind einige Hauptstädte, die Kanten stellen (Zug-) Verbindungen zwischen ihnen dar. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "g1 = nx.Graph()\n",
    "\n",
    "g1.add_node(\"Wien\")\n",
    "g1.add_node(\"Graz\")\n",
    "g1.add_node(\"Linz\")\n",
    "g1.add_node(\"Salzburg\")\n",
    "g1.add_node(\"Innsbruck\")\n",
    "g1.add_node(\"Villach\")\n",
    "g1.add_node(\"St. Pölten\")\n",
    "\n",
    "g1.add_edge(\"Graz\", \"Salzburg\")\n",
    "g1.add_edge(\"Wien\", \"Salzburg\")\n",
    "g1.add_path([\"Wien\", \"Graz\", \"Linz\", \"Salzburg\", \"Innsbruck\"])\n",
    "g1.add_path([\"St. Pölten\", \"Villach\", \"Graz\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot des Graphen, wobei mit `spring_layout` eine gleichmäßig verteilte Positionierung der Knoten berechnet wird.\n",
    "Anschließend werden nicht nur die Knoten und Kanten,\n",
    "sondern auch die Namen der Knoten geplottet."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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OXLt2DaUUCQkJpi4pixwJCGE+JARKIaUUfn5+7Ny5k/PnzzNhwgTatm3LN998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\nOU2zJj4V7QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcb0811db00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "pos = nx.spring_layout(g1)\n",
    "nx.draw_networkx_labels(g1, pos, font_size = 12)\n",
    "nx.draw(g1, pos)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ausgehend von diesem Graph lassen sich einige Kennzahlen und Parameter ausrechnen:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ist er zusammenhängend?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.is_connected(g1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Grad von Graz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.degree(g1, \"Graz\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Durchmesser des ganzen Graphs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.diameter(g1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Exzentrizität"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'Graz': 2,\n",
       " 'Innsbruck': 4,\n",
       " 'Linz': 3,\n",
       " 'Salzburg': 3,\n",
       " 'St. Pölten': 4,\n",
       " 'Villach': 3,\n",
       " 'Wien': 3}"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.eccentricity(g1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Kürzester Weg von Linz nach Innsbruck"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Linz', 'Salzburg', 'Innsbruck']"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.shortest_path(g1, \"Linz\", \"Innsbruck\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Es gibt außerdem eine große Bibliothek für Graphen.\n",
    "Hier wird ein Dodekaedergraph geladen und der 10-te Knoten entfernt."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PR1paGvbt20eb1r/h0aNHcHZ0hE92NuY14Off1Ue3uLgYFy5cqBLOBQUFeP/9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\nxAAAWEQQAwBg0X8BWB9KFit1MZoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcb0806b400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "g2=nx.dodecahedral_graph()\n",
    "g2.remove_node(10)\n",
    "nx.draw(g2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Durchmesser"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.diameter(g2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vergleich der Dichte beider Graphen:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.38095238095238093, 0.15789473684210525)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.density(g1), nx.density(g2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Histogramdaten für die Grade aller Knoten:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 0, 3, 16]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.degree_histogram(g2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gerichteter Graph\n",
    "\n",
    "Ein **gerichteter Graph** für die Wörter in einem Text."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "text = '''11:15 Restate my assumptions:\n",
    "1. Mathematics is the language of nature.\n",
    "2. Everything around us can be represented and understood through numbers. \n",
    "3. If you graph these numbers, patterns emerge.\n",
    "Therefore: There are patterns everywhere in nature.'''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import re\n",
    "words = re.compile(r'[a-zA-Z]+')\n",
    "tokens = words.findall(text)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "text_digraph = nx.MultiDiGraph()\n",
    "for t1, t2 in zip(tokens[:-1], tokens[1:]):\n",
    "    text_digraph.add_edge(t1, t2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PyDExMdSsWZOAgABCQ0Mfm5DbtGnD1q1b0etzc0f16TBkzBjCtdocFaq5i6G2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oAdKigoCC+88AIyMzOv2dbS0oKOjo4Rz9HZ7Qy76v7732EymVBRUTHsYy5fvoy6ujpH8B47dgwh\nISEwGo1Ys2YN3n777UFfPsazNVlZmLVjB/6Afy1jaH9XDgH4TwD9UJbs/BOUdbKd9QL4UKuFy6RJ\naNNquSwh3VGcRZ/GtdjYWOj1erzyyiswm82wWCxoamoaVH361VdfoaqqChaLBcXFxXB3d8fDDz98\nU8cLv/9+VLu5wX60/VAWZgcGt45WQWkN1wCwAjBDWTmqC8CX7u6Y5uuLWbNm4cqVKzh48CDeffdd\n1NfX45577kFKSgpEBOvWrcNbb72Fw4cP44knnkBBQQGam5sBABcuXEBlZSUAYOnSpWhubnacU0lJ\nCXp6eq45l7q6OuzIyUH1La4OVN3Xhx05Oejq6hr0JaGvrw9ffPEFduzYgaSkJEybNg3PP/88ent7\nsX79erS1taGxsRFvvPEGMjIyJkwIA4Cfnx+WLlmCPzqd7/cAHgVQAaAHwE9QhjA9Pszj/6jRYHlq\nKkxnzmBOfj5Orl6Nz1JScHL1aszJz0dLRwcqDhxgCNPoqHphnGgYoaGhjtmQRES6u7slMzNTZsyY\nId7e3hIfH+/YnpeXJxkZGbJy5UrR6/USHR0tDQ0NIx5r6PGmTp0qLhqNVNn6+FYB4geIHpD7ocw7\nbO//+9JWYett2ycFkEYoVdOJiYmD+nDLy8tlwYIF8uOPP0p9fb2sWLFCPDw8xM3NTaKjoyUwMFBc\nXFzEzc1NXF1dxdPTU2JjY+Wjjz6SxsZG+fjjjyUiIkK8vLxk48aNkpSUJIsXL5ZFixbJM888Iy+/\n/LIkxcbKq7exwMaciAh59NFHJTc3V+Lj48XDw0MSEhJk69at8tlnn8mFCxfG+J2+u8ZqHnSi28UJ\nPWhCy8/PR2trK/bt2zfqY6xKS0NMVRWeH8V/hdtZrs5sNuOHH35Aa2srvv/+e7S2tjr+tLW14d57\n70VYWJjjz3vvvYeWlpZBx4iEMn41FcrC8u8AiANQBuUS7JsAFtv2/QFAFoAGAPMAHAXg7euL9evX\nw2g0Ii4uDjqd7pbPYyKxX8q/2asIJgDJOh1yR9mvTnQz2EdMv3ibtm3DsupqpIxiZq1XpkzBp9u2\njep53d3dERkZicjIyGu2Wa1WdHV1DQrnof3GKwGkQZl20WS77wSApwGch9Kf/R8AOm3bngIwH8Bh\nAMehFJoFBQYiLy9vVK9/IrKH6YKcHGzp70fWMMVtwMjFV0RjgS1imtDuRIsYGP8tpUuXLsHT09Nx\newqAVwE8C+BBADuhhEcBAHubuR/KfMh/A3AZSiHaBdtjASAWwD8MBrS0to756x9v6uvrUbJrFw7e\nYB70TSy+oruAQUxkYx8GNB5bShaLBd999x1aW1vx/vvv46PKSmivXoUbgEtQWr9aKJekjzo9Tgvl\nS8M5AMugFCXZLQPwTUAA2s6evSvnMB6pMQ860VAMYiIn472l1NHRgYiICCQvXIglNTWOFvFGKKv9\njBTErlAqptkiJhp/2EdM5CQmJgYVBw44WkonnVpKcx54AIUqt5QuXboErVaLyLlzceLIEUy+fBl/\nvYnHBUFZPWgHlMvXJwCcBBDl5TWGr5aIbgaDmGgYt7Ni1FiaPXs2Nm/ejDfffBP/uHwZHgASr7O/\n81Qi+wGsBTANSihrXFxgCAsbw1dLRDeDl6aJJii1hl0R0Z3FICaaoOrq6rAsKemG01sOZQKwQKfD\np0eOsCKYaBzgFJdEE9RDDz2E/KIiJOt0jnHEN2IfdpVfVMQQJhonGMREE9i63/4WuUVFWKDToVij\nwY8j7NcL4FWNBgs4SxTRuMNL00Q/A+N92BURjYxBTPQzwgkqiCYeBjEREZGK2EdMRESkIgYxERGR\nihjEREREKmIQExERqYhBTEREpCIGMRERkYoYxERERCpiEBMREamIQUxERKQiBjEREZGKGMREREQq\nYhATERGpiEFMRESkIgYxERGRihjEREREKmIQExERqYhBTEREpCIGMRERkYoYxERERCpiEBMREamI\nQUxERKQiBjEREZGKGMREREQqYhATERGpiEFMRESkIgYxERGRihjEREREKmIQExERqYhBTEREpCIG\nMRERkYoYxERERCpiEBMREamIQUxERKQiBjEREZGKGMREREQqYhATERGpiEFMRESkIgYxERGRihjE\nREREKmIQExERqYhBTEREpCIGMRERkYoYxERERCpiEBMREamIQUxERKQiBjEREZGKGMREREQqYhAT\nERGpiEFMRESkIgYxERGRihjEREREKvonxa9vZGQ5v0sAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcb08139358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "nx.draw(text_digraph, with_labels = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Everything',\n",
       " 'around',\n",
       " 'us',\n",
       " 'can',\n",
       " 'be',\n",
       " 'represented',\n",
       " 'and',\n",
       " 'understood',\n",
       " 'through',\n",
       " 'numbers']"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.shortest_path(text_digraph, \"Everything\", \"numbers\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Baum (Tree)\n",
    "\n",
    "Ein Baum startet bei einem Wurzelknoten und verästelt sich ohne Schleifen zu bilden.\n",
    "Knoten ohne Kinder werden Blätter genannt."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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skKHHrO3btw9Tp05Fjx49sHLlSnYK30NeXh4mT56M0tJSfPzxx/D19RVdUqNUXl6OX3/9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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcb0040d6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rtree = nx.balanced_tree(2, 3)\n",
    "%matplotlib inline\n",
    "nx.draw(rtree)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.is_tree(rtree)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Liste der Blätter-Knoten (Grad ist 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[7, 8, 9, 10, 11, 12, 13, 14]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[ k for k, v in nx.degree(rtree).items() if v == 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Anaconda (Python 3)",
   "language": "python",
   "name": "anaconda3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}