{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# NetworkX"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Beispiel\n",
    "\n",
    "Im folgenden Beispiel erstellen wir eine einfache Benutzeroberfläche zum Erkunden von Zufallsgraphen mit [NetworkX](https://networkx.org)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import networkx as nx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zunächst erstellen wir einige Funktionen zur Erzeugung von Graphen, die alle die gleiche Signatur haben:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "def random_lobster(n, m, k, p):\n",
    "    return nx.random_lobster(n, p, p / m)\n",
    "\n",
    "\n",
    "def powerlaw_cluster(n, m, k, p):\n",
    "    return nx.powerlaw_cluster_graph(n, m, p)\n",
    "\n",
    "\n",
    "def erdos_renyi(n, m, k, p):\n",
    "    return nx.erdos_renyi_graph(n, p)\n",
    "\n",
    "\n",
    "def newman_watts_strogatz(n, m, k, p):\n",
    "    return nx.newman_watts_strogatz_graph(n, k, p)\n",
    "\n",
    "\n",
    "def plot_random_graph(n, m, k, p, generator):\n",
    "    g = generator(n, m, k, p)\n",
    "    nx.draw(g)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nun erstellen wir Schieberegler und ein Aufklappmenü zur Interaktion mit Plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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       "version_major": 2,
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      },
      "text/plain": [
       "interactive(children=(IntSlider(value=16, description='n', max=30, min=2), IntSlider(value=5, description='m',…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from ipywidgets import interact\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "interact(plot_random_graph, n=(2,30), m=(1,10), k=(1,10), p=(0.0, 1.0, 0.001),\n",
    "         generator={\n",
    "             'lobster': random_lobster,\n",
    "             'power law': powerlaw_cluster,\n",
    "             'Newman-Watts-Strogatz': newman_watts_strogatz,\n",
    "             u'Erdős-Rényi': erdos_renyi,\n",
    "         });"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Graphviz\n",
    "\n",
    "Graphviz kann auf zweierlei Arten verwendet werden:\n",
    "\n",
    "* zusammen mit Matplotlib und [pygraphviz](https://pygraphviz.github.io/), siehe [Drawing NetworkX with Matplotlib](https://networkx.org/documentation/stable/reference/drawing.html#module-networkx.drawing.nx_pylab)\n",
    "* zusammen mit Graphviz AGraph, siehe [Drawing NetworkX with Graphviz AGraph](https://networkx.org/documentation/stable/reference/drawing.html#module-networkx.drawing.nx_agraph)"
   ]
  }
 ],
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  "latex_envs": {
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   "hotkeys": {
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\n",
          "text/plain": "<Figure size 432x288 with 1 Axes>"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ]
      }
     },
     "1225e73d7f49415c93a20146b8ad163e": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "DropdownModel",
      "state": {
       "_options_labels": [
        "lobster",
        "power law",
        "Newman-Watts-Strogatz",
        "Erdős-Rényi"
       ],
       "description": "generator",
       "index": 0,
       "layout": "IPY_MODEL_c8f1db1eeaf44f219e9ae591349636bc",
       "style": "IPY_MODEL_847a92a838204728a8c375a24bd60c9f"
      }
     },
     "171f5f88cdd34c4ab89a1fed974897d3": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_d46f11e05bb74affbf853cba8d4e314e",
       "outputs": [
        {
         "data": {
          "image/png": 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\n",
          "text/plain": "<Figure size 432x288 with 1 Axes>"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ]
      }
     },
     "1907794a6a39476d97ad5b1100631f09": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "1ce10e45f1d74988b9fc366ad4277c7b": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "SliderStyleModel",
      "state": {
       "description_width": ""
      }
     },
     "299879dad0e94189852fdd57c0b8df05": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "FloatSliderModel",
      "state": {
       "description": "p",
       "layout": "IPY_MODEL_0fde4739410f4aca96d005441fa016a0",
       "max": 1,
       "step": 0.001,
       "style": "IPY_MODEL_98feeb90e7db4894bce7eb6f8827caee",
       "value": 0.5
      }
     },
     "2bfbbd1d76f34ea1ab4d78d227417a64": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_72cc7d94002d4cb180d00ed073caa39f",
       "outputs": [
        {
         "data": {
          "image/png": 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