{ "cells": [ { "cell_type": "markdown", "id": "91a56e0a", "metadata": {}, "source": [ "# Six degrees of separation" ] }, { "cell_type": "markdown", "id": "5a6d9136", "metadata": {}, "source": [ "We can revisit Milgram's experience on small worlds. Cf [Kleinberg's Grid Unchained](https://inria.hal.science/hal-02052607/document) for details." ] }, { "cell_type": "code", "execution_count": 4, "id": "0e71153b", "metadata": {}, "outputs": [], "source": [ "from kleinberg_grid_simulator import compute_edt, parallelize\n", "from collections import defaultdict\n", "from matplotlib import pyplot as plt" ] }, { "cell_type": "code", "execution_count": 2, "id": "69465444", "metadata": {}, "outputs": [], "source": [ "rr = [r/10 for r in range(0, 31)]\n", "values = [{'n': 8500, 'r': r, **pq} for r in rr for pq in [{'p': 1, 'q': 600}, {'p': 10, 'q': 380}, {'p': 15, 'q': 120}]]" ] }, { "cell_type": "code", "execution_count": 3, "id": "00b7a48f", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|███████████████████████████████████████████████████████████████████████████████████| 93/93 [00:21<00:00, 4.31it/s]\n" ] } ], "source": [ "res = parallelize(values)" ] }, { "cell_type": "code", "execution_count": 5, "id": "655b5e5c", "metadata": {}, "outputs": [], "source": [ "edts = defaultdict(list)\n", "for re in res:\n", " label = f\"p={re.p}, q={re.q}\"\n", " edts[label].append(re.edt)" ] }, { "cell_type": "code", "execution_count": 11, "id": "7eec9786", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for label, y in edts.items():\n", " plt.plot(rr, y, label=label)\n", "plt.plot([0, 3], [6, 6], '-.', color='black')\n", "plt.xlabel('$r$')\n", "plt.ylabel('Expected Delivery Time')\n", "plt.xlim([0, 3])\n", "plt.ylim([0, 20])\n", "plt.legend()\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.9" } }, "nbformat": 4, "nbformat_minor": 5 }