gerritjandebruin/powerlaw.ipynb

## powerlaw.ipynb
{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "powerlaw.ipynb",
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/gerritjandebruin/d35038cbf7a26ca5962e2150bb8c44a6/powerlaw.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XomdVPuiRLFJ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1pNP6vmHQgWk",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "degree_dict = {1: 117181, 2: 39499, 3: 19347, 4: 11394, 5: 7584, 6: 5361, 7: 3863, 8: 2991, 9: 2384, 10: 1895, 11: 1492, 12: 1255, 13: 1076, 14: 892, 15: 684, 16: 659, 17: 536, 18: 499, 19: 427, 20: 417, 21: 336, 22: 286, 23: 251, 24: 224, 25: 223, 26: 189, 27: 177, 28: 177, 29: 168, 30: 141, 31: 115, 32: 120, 33: 109, 34: 79, 35: 109, 36: 60, 37: 66, 38: 66, 39: 78, 40: 59, 41: 59, 42: 49, 43: 37, 44: 44, 45: 47, 46: 38, 47: 36, 48: 26, 49: 31, 50: 29, 51: 33, 52: 28, 53: 23, 54: 21, 55: 22, 56: 26, 57: 21, 58: 14, 59: 16, 60: 19, 61: 18, 62: 12, 63: 15, 64: 13, 65: 14, 66: 12, 67: 10, 68: 14, 69: 15, 70: 5, 71: 11, 72: 14, 73: 9, 74: 10, 75: 9, 76: 7, 77: 7, 78: 5, 79: 12, 80: 11, 81: 3, 82: 3, 83: 11, 84: 8, 85: 4, 86: 12, 87: 11, 88: 8, 89: 6, 90: 9, 91: 4, 92: 5, 93: 3, 94: 8, 95: 11, 96: 6, 97: 5, 98: 7, 99: 6, 100: 3, 102: 2, 103: 6, 104: 6, 105: 1, 106: 7, 107: 5, 108: 6, 109: 7, 110: 7, 111: 3, 112: 4, 113: 2, 114: 3, 115: 1, 116: 5, 117: 4, 118: 5, 119: 5, 120: 2, 121: 4, 122: 5, 123: 2, 124: 5, 125: 3, 126: 3, 127: 5, 128: 5, 129: 2, 132: 4, 133: 4, 134: 3, 135: 2, 136: 5, 137: 4, 138: 1, 139: 3, 140: 2, 141: 1, 143: 2, 145: 2, 146: 3, 147: 1, 148: 1, 149: 2, 150: 5, 151: 4, 152: 2, 153: 2, 154: 3, 155: 3, 156: 2, 157: 1, 158: 1, 159: 1, 160: 4, 161: 2, 164: 3, 165: 2, 166: 2, 167: 4, 168: 2, 169: 1, 170: 1, 171: 1, 173: 1, 174: 2, 175: 1, 177: 1, 178: 1, 179: 1, 182: 2, 184: 4, 189: 2, 190: 1, 191: 1, 193: 1, 194: 2, 195: 2, 196: 2, 199: 4, 201: 2, 202: 1, 205: 3, 206: 3, 207: 3, 208: 2, 209: 2, 210: 4, 211: 1, 212: 2, 213: 1, 214: 3, 216: 2, 217: 1, 218: 3, 220: 1, 223: 1, 224: 2, 226: 3, 228: 4, 231: 1, 232: 1, 233: 1, 235: 1, 236: 1, 239: 2, 240: 1, 242: 1, 243: 1, 246: 1, 247: 1, 251: 2, 252: 1, 253: 1, 254: 3, 256: 3, 257: 2, 261: 1, 262: 1, 263: 1, 264: 1, 267: 2, 269: 1, 271: 1, 275: 1, 276: 2, 279: 1, 283: 1, 284: 1, 288: 1, 289: 1, 290: 2, 291: 1, 292: 1, 293: 1, 294: 2, 296: 1, 299: 1, 300: 1, 301: 1, 302: 1, 305: 1, 307: 1, 311: 1, 313: 1, 315: 1, 317: 1, 318: 1, 326: 1, 330: 1, 334: 2, 338: 1, 346: 1, 349: 1, 357: 1, 362: 1, 366: 1, 367: 1, 369: 1, 373: 1, 387: 1, 388: 1, 391: 2, 393: 1, 398: 1, 402: 1, 405: 1, 420: 1, 421: 1, 424: 1, 433: 1, 434: 1, 441: 2, 445: 1, 447: 1, 448: 1, 461: 1, 470: 1, 471: 1, 475: 1, 482: 1, 488: 1, 490: 2, 495: 1, 497: 1, 503: 1, 515: 1, 519: 1, 526: 1, 540: 1, 541: 1, 543: 1, 554: 1, 555: 1, 575: 1, 593: 1, 595: 1, 602: 1, 612: 1, 636: 1, 639: 1, 643: 1, 649: 1, 650: 1, 651: 1, 684: 1, 706: 1, 708: 1, 712: 1, 714: 1, 722: 1, 726: 1, 730: 1, 778: 1, 812: 1, 828: 1, 829: 1, 831: 1, 864: 1, 890: 1, 895: 1, 906: 1, 923: 1, 973: 1, 974: 1, 992: 1, 1038: 1, 1063: 1, 1066: 1, 1155: 1, 1172: 1, 1234: 1, 1267: 1, 1443: 1, 1497: 1, 2791: 1, 2947: 1}\n",
        "degree_list = [degree_dict.get(i+1, 0) for i in range(max(degree_dict.keys()))]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "O-TOYtHyQjSj",
        "colab_type": "code",
        "outputId": "29dd3992-9671-42c9-b0ef-ae22e2f4af39",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 289
        }
      },
      "source": [
        "counts, bins = np.histogram(\n",
        "    degree_list,\n",
        "    bins = np.round(np.logspace(start=np.log10(2), stop=np.log10(len(degree_list)), num=12))\n",
        ")\n",
        "x = bins[:-1] + np.diff(bins)/2\n",
        "y = counts\n",
        "p0, p1 = np.polyfit(np.log10(x), np.log10(y), 1)\n",
        "y_fit = 10**(p0*np.log10(x) + p1)\n",
        "\n",
        "plt.plot(x, y, marker=\"o\", ls=\"\")\n",
        "plt.plot(x, y_fit)\n",
        "\n",
        "plt.xscale(\"log\")\n",
        "plt.xlabel(\"Number of neighbours\")\n",
        "\n",
        "plt.yscale(\"log\")\n",
        "plt.ylim(1, 1e2)\n",
        "plt.ylabel(\"Frequency\")\n",
        "\n",
        "plt.tick_params(which=\"both\");"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JcNCTEOOLfdc",
        "colab_type": "text"
      },
      "source": [
        "$p(k) = c k^{-\\gamma}$\n",
        "\n",
        "$log10(p(k)) = log10(c k^{-\\gamma}) = log10(c)-\\gamma log(k)$ \n",
        "\n",
        "$y = p0*x + p1$\n",
        "\n",
        "with:\n",
        "\n",
        "$x = log10(k)$\n",
        "\n",
        "$y = log10(p(k))$\n",
        "\n",
        "$p0 = -\\gamma$ (powerlaw exponent)\n",
        "\n",
        "$p1 = log10(c)$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cY0UFav4RKAy",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "d86f046b-bc19-4202-ab4a-101816b47ce1"
      },
      "source": [
        "print(f'Exponent: {-p0}')"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Exponent: -0.4414624907852282\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Tfw1ZD0VJ8X8",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}
	{
	"nbformat": 4,
	"nbformat_minor": 0,
	"metadata": {
	"colab": {
	"name": "powerlaw.ipynb",
	"provenance": []
	},
	"kernelspec": {
	"name": "python3",
	"display_name": "Python 3"
	}
	},
	"cells": [
	{
	"cell_type": "markdown",
	"metadata": {
	"id": "view-in-github",
	"colab_type": "text"
	},
	"source": [
	"<a href=\"https://colab.research.google.com/gist/gerritjandebruin/d35038cbf7a26ca5962e2150bb8c44a6/powerlaw.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
	]
	},
	{
	"cell_type": "code",
	"metadata": {
	"id": "XomdVPuiRLFJ",
	"colab_type": "code",
	"colab": {}
	},
	"source": [
	"import numpy as np\n",
	"import matplotlib.pyplot as plt"
	],
	"execution_count": 0,
	"outputs": []
	},
	{
	"cell_type": "code",
	"metadata": {
	"id": "1pNP6vmHQgWk",
	"colab_type": "code",
	"colab": {}
	},
	"source": [
	"degree_dict = {1: 117181, 2: 39499, 3: 19347, 4: 11394, 5: 7584, 6: 5361, 7: 3863, 8: 2991, 9: 2384, 10: 1895, 11: 1492, 12: 1255, 13: 1076, 14: 892, 15: 684, 16: 659, 17: 536, 18: 499, 19: 427, 20: 417, 21: 336, 22: 286, 23: 251, 24: 224, 25: 223, 26: 189, 27: 177, 28: 177, 29: 168, 30: 141, 31: 115, 32: 120, 33: 109, 34: 79, 35: 109, 36: 60, 37: 66, 38: 66, 39: 78, 40: 59, 41: 59, 42: 49, 43: 37, 44: 44, 45: 47, 46: 38, 47: 36, 48: 26, 49: 31, 50: 29, 51: 33, 52: 28, 53: 23, 54: 21, 55: 22, 56: 26, 57: 21, 58: 14, 59: 16, 60: 19, 61: 18, 62: 12, 63: 15, 64: 13, 65: 14, 66: 12, 67: 10, 68: 14, 69: 15, 70: 5, 71: 11, 72: 14, 73: 9, 74: 10, 75: 9, 76: 7, 77: 7, 78: 5, 79: 12, 80: 11, 81: 3, 82: 3, 83: 11, 84: 8, 85: 4, 86: 12, 87: 11, 88: 8, 89: 6, 90: 9, 91: 4, 92: 5, 93: 3, 94: 8, 95: 11, 96: 6, 97: 5, 98: 7, 99: 6, 100: 3, 102: 2, 103: 6, 104: 6, 105: 1, 106: 7, 107: 5, 108: 6, 109: 7, 110: 7, 111: 3, 112: 4, 113: 2, 114: 3, 115: 1, 116: 5, 117: 4, 118: 5, 119: 5, 120: 2, 121: 4, 122: 5, 123: 2, 124: 5, 125: 3, 126: 3, 127: 5, 128: 5, 129: 2, 132: 4, 133: 4, 134: 3, 135: 2, 136: 5, 137: 4, 138: 1, 139: 3, 140: 2, 141: 1, 143: 2, 145: 2, 146: 3, 147: 1, 148: 1, 149: 2, 150: 5, 151: 4, 152: 2, 153: 2, 154: 3, 155: 3, 156: 2, 157: 1, 158: 1, 159: 1, 160: 4, 161: 2, 164: 3, 165: 2, 166: 2, 167: 4, 168: 2, 169: 1, 170: 1, 171: 1, 173: 1, 174: 2, 175: 1, 177: 1, 178: 1, 179: 1, 182: 2, 184: 4, 189: 2, 190: 1, 191: 1, 193: 1, 194: 2, 195: 2, 196: 2, 199: 4, 201: 2, 202: 1, 205: 3, 206: 3, 207: 3, 208: 2, 209: 2, 210: 4, 211: 1, 212: 2, 213: 1, 214: 3, 216: 2, 217: 1, 218: 3, 220: 1, 223: 1, 224: 2, 226: 3, 228: 4, 231: 1, 232: 1, 233: 1, 235: 1, 236: 1, 239: 2, 240: 1, 242: 1, 243: 1, 246: 1, 247: 1, 251: 2, 252: 1, 253: 1, 254: 3, 256: 3, 257: 2, 261: 1, 262: 1, 263: 1, 264: 1, 267: 2, 269: 1, 271: 1, 275: 1, 276: 2, 279: 1, 283: 1, 284: 1, 288: 1, 289: 1, 290: 2, 291: 1, 292: 1, 293: 1, 294: 2, 296: 1, 299: 1, 300: 1, 301: 1, 302: 1, 305: 1, 307: 1, 311: 1, 313: 1, 315: 1, 317: 1, 318: 1, 326: 1, 330: 1, 334: 2, 338: 1, 346: 1, 349: 1, 357: 1, 362: 1, 366: 1, 367: 1, 369: 1, 373: 1, 387: 1, 388: 1, 391: 2, 393: 1, 398: 1, 402: 1, 405: 1, 420: 1, 421: 1, 424: 1, 433: 1, 434: 1, 441: 2, 445: 1, 447: 1, 448: 1, 461: 1, 470: 1, 471: 1, 475: 1, 482: 1, 488: 1, 490: 2, 495: 1, 497: 1, 503: 1, 515: 1, 519: 1, 526: 1, 540: 1, 541: 1, 543: 1, 554: 1, 555: 1, 575: 1, 593: 1, 595: 1, 602: 1, 612: 1, 636: 1, 639: 1, 643: 1, 649: 1, 650: 1, 651: 1, 684: 1, 706: 1, 708: 1, 712: 1, 714: 1, 722: 1, 726: 1, 730: 1, 778: 1, 812: 1, 828: 1, 829: 1, 831: 1, 864: 1, 890: 1, 895: 1, 906: 1, 923: 1, 973: 1, 974: 1, 992: 1, 1038: 1, 1063: 1, 1066: 1, 1155: 1, 1172: 1, 1234: 1, 1267: 1, 1443: 1, 1497: 1, 2791: 1, 2947: 1}\n",
	"degree_list = [degree_dict.get(i+1, 0) for i in range(max(degree_dict.keys()))]"
	],
	"execution_count": 0,
	"outputs": []
	},
	{
	"cell_type": "code",
	"metadata": {
	"id": "O-TOYtHyQjSj",
	"colab_type": "code",
	"outputId": "29dd3992-9671-42c9-b0ef-ae22e2f4af39",
	"colab": {
	"base_uri": "https://localhost:8080/",
	"height": 289
	}
	},
	"source": [
	"counts, bins = np.histogram(\n",
	" degree_list,\n",
	" bins = np.round(np.logspace(start=np.log10(2), stop=np.log10(len(degree_list)), num=12))\n",
	")\n",
	"x = bins[:-1] + np.diff(bins)/2\n",
	"y = counts\n",
	"p0, p1 = np.polyfit(np.log10(x), np.log10(y), 1)\n",
	"y_fit = 10*(p0np.log10(x) + p1)\n",
	"\n",
	"plt.plot(x, y, marker=\"o\", ls=\"\")\n",
	"plt.plot(x, y_fit)\n",
	"\n",
	"plt.xscale(\"log\")\n",
	"plt.xlabel(\"Number of neighbours\")\n",
	"\n",
	"plt.yscale(\"log\")\n",
	"plt.ylim(1, 1e2)\n",
	"plt.ylabel(\"Frequency\")\n",
	"\n",
	"plt.tick_params(which=\"both\");"
	],
	"execution_count": 9,
	"outputs": [
	{
	"output_type": "display_data",
	"data": {
	"image/png": 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\n",
	"text/plain": [
	"<Figure size 432x288 with 1 Axes>"
	]
	},
	"metadata": {
	"tags": [],
	"needs_background": "light"
	}
	}
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {
	"id": "JcNCTEOOLfdc",
	"colab_type": "text"
	},
	"source": [
	"$p(k) = c k^{-\\gamma}$\n",
	"\n",
	"$log10(p(k)) = log10(c k^{-\\gamma}) = log10(c)-\\gamma log(k)$ \n",
	"\n",
	"$y = p0*x + p1$\n",
	"\n",
	"with:\n",
	"\n",
	"$x = log10(k)$\n",
	"\n",
	"$y = log10(p(k))$\n",
	"\n",
	"$p0 = -\\gamma$ (powerlaw exponent)\n",
	"\n",
	"$p1 = log10(c)$"
	]
	},
	{
	"cell_type": "code",
	"metadata": {
	"id": "cY0UFav4RKAy",
	"colab_type": "code",
	"colab": {
	"base_uri": "https://localhost:8080/",
	"height": 34
	},
	"outputId": "d86f046b-bc19-4202-ab4a-101816b47ce1"
	},
	"source": [
	"print(f'Exponent: {-p0}')"
	],
	"execution_count": 11,
	"outputs": [
	{
	"output_type": "stream",
	"text": [
	"Exponent: -0.4414624907852282\n"
	],
	"name": "stdout"
	}
	]
	},
	{
	"cell_type": "code",
	"metadata": {
	"id": "Tfw1ZD0VJ8X8",
	"colab_type": "code",
	"colab": {}
	},
	"source": [
	""
	],
	"execution_count": 0,
	"outputs": []
	}
	]
	}