network_ana

Complex Network Anlysis
git clone git://popovic.xyz/network_ana.git
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main.ipynb (99446B)

      1 {
      2  "cells": [
      3   {
      4    "cell_type": "code",
      5    "execution_count": 135,
      6    "id": "2ce8d8f8",
      7    "metadata": {},
      8    "outputs": [],
      9    "source": [
     10     "import random\n",
     11     "import numpy as np\n",
     12     "import networkx as nx\n",
     13     "import numpy as np\n",
     14     "import matplotlib.pyplot as plt\n",
     15     "import itertools"
     16    ]
     17   },
     18   {
     19    "cell_type": "markdown",
     20    "id": "53ee1eaa",
     21    "metadata": {},
     22    "source": [
     23     "# Exercise 1"
     24    ]
     25   },
     26   {
     27    "cell_type": "code",
     28    "execution_count": 136,
     29    "id": "ef3299d8",
     30    "metadata": {},
     31    "outputs": [],
     32    "source": [
     33     "d = 6\n",
     34     "x = [i for i in range(1, d+1)]\n",
     35     "n = [1000, 10000, 100000]\n",
     36     "\n",
     37     "def dice_throw(n, weights):\n",
     38     "    dice = random.choices(range(1, d+1), weights=weights, k=n)\n",
     39     "    x = list(range(1, d+1))\n",
     40     "    y = np.array([dice.count(i)/n for i in x])\n",
     41     "    return y\n",
     42     "weights = [1/6 for i in range(1, d+1)]\n",
     43     "y_vals = np.array([dice_throw(n_i, weights) for n_i in n])\n",
     44     "y = np.array([np.mean(y_vals[:, i]) for i in range(d)])\n",
     45     "\n",
     46     "weights_mod = [11/75, 11/75, 11/75, 11/75, 11/75, 4/15]\n",
     47     "y_mod_vals = np.array([dice_throw(n_i, weights_mod) for n_i in n])\n",
     48     "y_mod = np.array([np.mean(y_mod_vals[:, i]) for i in range(d)])"
     49    ]
     50   },
     51   {
     52    "cell_type": "markdown",
     53    "id": "fe2fba6d",
     54    "metadata": {},
     55    "source": [
     56     "## Certainly biased die (brute force)"
     57    ]
     58   },
     59   {
     60    "cell_type": "code",
     61    "execution_count": 147,
     62    "id": "af1b5a42",
     63    "metadata": {},
     64    "outputs": [
     65     {
     66      "name": "stdout",
     67      "output_type": "stream",
     68      "text": [
     69       "Certainly biased die with 0.04% uncertainty condition: 41.29 throws\n"
     70      ]
     71     }
     72    ],
     73    "source": [
     74     "sol = []\n",
     75     "p = 0.96\n",
     76     "for i in range(100):\n",
     77     "    for throws in range(1, 50): # dice 'throws'\n",
     78     "        grab = []\n",
     79     "        for j in range(100): # 'throws'-number of times - 'j' number of times \n",
     80     "            y_n_vals = np.array(dice_throw(throws, weights_mod))\n",
     81     "            y_15 = np.mean(y_n_vals[:5])\n",
     82     "            y_6 = y_n_vals[-1]\n",
     83     "            grab.append((y_6 - y_15) > 0)  # check error difference\n",
     84     "        if np.mean(grab) > p:\n",
     85     "            sol.append(throws)\n",
     86     "            break\n",
     87     "print(f\"Certainly biased die with {round(1-p, 2)}% uncertainty condition: {round(np.mean(sol), 2)} throws\")"
     88    ]
     89   },
     90   {
     91    "cell_type": "markdown",
     92    "id": "a200b2c8",
     93    "metadata": {},
     94    "source": [
     95     "## Plots"
     96    ]
     97   },
     98   {
     99    "cell_type": "code",
    100    "execution_count": 148,
    101    "id": "2518787c",
    102    "metadata": {},
    103    "outputs": [
    104     {
    105      "name": "stdout",
    106      "output_type": "stream",
    107      "text": [
    108       "\n"
    109      ]
    110     },
    111     {
    112      "data": {
    113       "image/png": 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\n",
    114       "text/plain": [
    115        "<Figure size 1224x432 with 3 Axes>"
    116       ]
    117      },
    118      "metadata": {
    119       "needs_background": "light"
    120      },
    121      "output_type": "display_data"
    122     }
    123    ],
    124    "source": [
    125     "fig, ax = plt.subplots(1, 3, figsize=(17, 6))\n",
    126     "ax[0].bar(x, y,\n",
    127     "        alpha=0.5,\n",
    128     "        yerr=[np.std(y_vals[:,i]) for i in range(d)],\n",
    129     "        capsize=3,\n",
    130     "        ecolor='black',\n",
    131     "        align='center'\n",
    132     "       )\n",
    133     "ax[0].set_yticks([1/6])\n",
    134     "ax[0].set_yticklabels([r\"$\\frac{1}{6}$\"], fontsize=15)\n",
    135     "ax[0].set_xlabel(r\"$p_i$\", fontsize=15)\n",
    136     "\n",
    137     "ax[1].bar(x, y_mod,\n",
    138     "        alpha=0.5,\n",
    139     "        yerr=[np.std(y_mod_vals[:,i]) for i in range(d)],\n",
    140     "        capsize=3,\n",
    141     "        ecolor='black',\n",
    142     "        align='center'\n",
    143     "       )\n",
    144     "ax[1].set_yticks([11/75,1/6, 4/15])\n",
    145     "ax[1].set_yticklabels([r\"$\\frac{11}{75}$\",r\"$\\frac{1}{6}$\",r\"$\\frac{4}{15}$\"], fontsize=15)\n",
    146     "ax[1].set_xlabel(r\"$p_i$\", fontsize=15)\n",
    147     "\n",
    148     "ax[2].bar([1, 2], [np.mean(y_n_vals[:5]), y_n_vals[-1]],\n",
    149     "        alpha=0.5,\n",
    150     "        capsize=3,\n",
    151     "        ecolor='black',\n",
    152     "        align='center'\n",
    153     "       )\n",
    154     "ax[2].set_yticks([11/75,1/6, 4/15])\n",
    155     "ax[2].set_yticklabels([r\"$\\frac{11}{75}$\",r\"$\\frac{1}{6}$\", r\"$\\frac{4}{15}$\"], fontsize=15)\n",
    156     "ax[2].set_xticks([1, 2])\n",
    157     "ax[2].set_xticklabels([r\"$1...5$\", r\"$6$\"])\n",
    158     "ax[2].set_xlabel(r\"$p_i$\", fontsize=15)\n",
    159     "ax[2].set_title(f\"{throws} Throws\")\n",
    160     "print('')"
    161    ]
    162   },
    163   {
    164    "cell_type": "markdown",
    165    "id": "fb8e1745",
    166    "metadata": {},
    167    "source": [
    168     "# Exercise 2: random graphs"
    169    ]
    170   },
    171   {
    172    "cell_type": "code",
    173    "execution_count": 149,
    174    "id": "c4a8f0cd",
    175    "metadata": {},
    176    "outputs": [],
    177    "source": [
    178     "p = np.linspace(0, 1, 100)\n",
    179     "n = 500\n",
    180     "k_avg = []\n",
    181     "connected = []\n",
    182     "k_max = []\n",
    183     "spl = []\n",
    184     "for p_i in p:\n",
    185     "    G = nx.gnp_random_graph(n, p_i)\n",
    186     "    k_s = list(dict(G.degree()).values())\n",
    187     "    \n",
    188     "    if nx.is_connected(G)==False:\n",
    189     "        spl.append(0)\n",
    190     "    else:\n",
    191     "        spl.append(nx.average_shortest_path_length(G))\n",
    192     "        \n",
    193     "    connected.append(n - k_s.count(0))\n",
    194     "    k_max.append(max(k_s))\n",
    195     "    k_avg.append(np.mean(k_s))"
    196    ]
    197   },
    198   {
    199    "cell_type": "code",
    200    "execution_count": 150,
    201    "id": "22a012ef",
    202    "metadata": {
    203     "scrolled": false
    204    },
    205    "outputs": [
    206     {
    207      "data": {
    208       "image/png": 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\n",
    209       "text/plain": [
    210        "<Figure size 720x864 with 6 Axes>"
    211       ]
    212      },
    213      "metadata": {
    214       "needs_background": "light"
    215      },
    216      "output_type": "display_data"
    217     }
    218    ],
    219    "source": [
    220     "fig, ax = plt.subplots(3 ,2, figsize=(10, 12))\n",
    221     "ax[0][0].plot(p, k_avg)\n",
    222     "ax[0][0].set_xlabel(r\"$p_i$\", fontsize=15)\n",
    223     "ax[0][0].set_ylabel(r\"$<k>$\", fontsize=15)\n",
    224     "\n",
    225     "ax[0][1].plot(p, k_max)\n",
    226     "ax[0][1].set_xlabel(r\"$p_i$\", fontsize=15)\n",
    227     "ax[0][1].set_ylabel(r\"$k_{max}$\", fontsize=15)\n",
    228     "\n",
    229     "ax[1][0].plot(p, connected)\n",
    230     "ax[1][0].set_xlabel(r\"$p_i$\", fontsize=15)\n",
    231     "ax[1][0].set_ylabel(\"# connected\", fontsize=15)\n",
    232     "\n",
    233     "ax[1][1].plot(p, spl)\n",
    234     "ax[1][1].set_xlabel(r\"$p_i$\", fontsize=15)\n",
    235     "ax[1][1].set_ylabel(\"spl\", fontsize=15)\n",
    236     "\n",
    237     "ax[2][0].plot(k_avg, k_max)\n",
    238     "ax[2][0].set_xlabel(r\"$<k>$\", fontsize=15)\n",
    239     "ax[2][0].set_ylabel(r\"$k_{max}$\", fontsize=15)\n",
    240     "\n",
    241     "ax[2][1].plot(k_avg, spl)\n",
    242     "ax[2][1].set_xlabel(r\"$<k>$\", fontsize=15)\n",
    243     "ax[2][1].set_ylabel(\"spl\", fontsize=15)\n",
    244     "plt.tight_layout()"
    245    ]
    246   },
    247   {
    248    "cell_type": "markdown",
    249    "id": "72292481",
    250    "metadata": {},
    251    "source": [
    252     "# Exercise 3"
    253    ]
    254   },
    255   {
    256    "cell_type": "code",
    257    "execution_count": 151,
    258    "id": "d5297e62",
    259    "metadata": {},
    260    "outputs": [
    261     {
    262      "data": {
    263       "text/plain": [
    264        "<matplotlib.legend.Legend at 0x7f5648542820>"
    265       ]
    266      },
    267      "execution_count": 151,
    268      "metadata": {},
    269      "output_type": "execute_result"
    270     },
    271     {
    272      "data": {
    273       "image/png": 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\n",
    274       "text/plain": [
    275        "<Figure size 576x360 with 1 Axes>"
    276       ]
    277      },
    278      "metadata": {
    279       "needs_background": "light"
    280      },
    281      "output_type": "display_data"
    282     }
    283    ],
    284    "source": [
    285     "sizes = list(itertools.combinations([i for i in range(1, 25)], 2))\n",
    286     "spl_l= []\n",
    287     "k_avg_l = []\n",
    288     "for s in sizes:\n",
    289     "    G_l = nx.grid_2d_graph(*s)\n",
    290     "    k_s = list(dict(G_l.degree()).values())\n",
    291     "    \n",
    292     "    if nx.is_connected(G)==False:\n",
    293     "        spl_l.append(0)\n",
    294     "    else:\n",
    295     "        spl_l.append(nx.average_shortest_path_length(G_l))\n",
    296     "    k_avg_l.append(np.mean(k_s))\n",
    297     "    \n",
    298     "plt.figure(figsize=(8, 5))\n",
    299     "plt.plot(k_avg_l, spl_l, label='Grid Graph')\n",
    300     "plt.plot(k_avg, spl, label='Random Graph')\n",
    301     "plt.xlabel(r\"$<k>$\", fontsize=15)\n",
    302     "plt.ylabel(\"spl\", fontsize=15)\n",
    303     "plt.legend(loc='best')"
    304    ]
    305   },
    306   {
    307    "cell_type": "code",
    308    "execution_count": 152,
    309    "id": "de87797b",
    310    "metadata": {},
    311    "outputs": [],
    312    "source": []
    313   },
    314   {
    315    "cell_type": "code",
    316    "execution_count": null,
    317    "id": "b17d9239",
    318    "metadata": {},
    319    "outputs": [],
    320    "source": [
    321     "    "
    322    ]
    323   },
    324   {
    325    "cell_type": "code",
    326    "execution_count": null,
    327    "id": "3f036f76",
    328    "metadata": {},
    329    "outputs": [],
    330    "source": []
    331   },
    332   {
    333    "cell_type": "code",
    334    "execution_count": null,
    335    "id": "ecb080d0",
    336    "metadata": {},
    337    "outputs": [],
    338    "source": []
    339   },
    340   {
    341    "cell_type": "code",
    342    "execution_count": null,
    343    "id": "71ea711d",
    344    "metadata": {},
    345    "outputs": [],
    346    "source": []
    347   },
    348   {
    349    "cell_type": "code",
    350    "execution_count": null,
    351    "id": "93cef28f",
    352    "metadata": {},
    353    "outputs": [],
    354    "source": []
    355   },
    356   {
    357    "cell_type": "code",
    358    "execution_count": null,
    359    "id": "3b608f08",
    360    "metadata": {},
    361    "outputs": [],
    362    "source": []
    363   }
    364  ],
    365  "metadata": {
    366   "kernelspec": {
    367    "display_name": "Python 3 (ipykernel)",
    368    "language": "python",
    369    "name": "python3"
    370   },
    371   "language_info": {
    372    "codemirror_mode": {
    373     "name": "ipython",
    374     "version": 3
    375    },
    376    "file_extension": ".py",
    377    "mimetype": "text/x-python",
    378    "name": "python",
    379    "nbconvert_exporter": "python",
    380    "pygments_lexer": "ipython3",
    381    "version": "3.9.7"
    382   }
    383  },
    384  "nbformat": 4,
    385  "nbformat_minor": 5
    386 }