Figure_S4_S5_synthetic_structures.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "53ced03e",
   "metadata": {},
   "source": [
    "# Synchronization stability of simplicial complexes generated from scale-free and small-world networks"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ccaf1528",
   "metadata": {},
   "source": [
    "This code was used for the analysis presented in  \n",
    "\"Do higher-order interactions promote synchronization?\"  \n",
    "by Yuanzhao Zhang, Maxime Lucas, and Federico Battiston"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a568937e",
   "metadata": {},
   "outputs": [],
   "source": [
    "from pathlib import Path\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import networkx as nx\n",
    "import numpy as np\n",
    "import seaborn as sb\n",
    "from labellines import labelLines\n",
    "from tqdm import tqdm\n",
    "\n",
    "import xgi\n",
    "from utils import (\n",
    "    compute_eigenvalues_multi,\n",
    "    flag_complex_d2,\n",
    ")\n",
    "\n",
    "sb.set_theme(style=\"ticks\", context=\"paper\")\n",
    "\n",
    "fig_dir = \"figures/\"\n",
    "results_dir = \"results/\"\n",
    "\n",
    "Path(fig_dir).mkdir(parents=True, exist_ok=True)\n",
    "Path(results_dir).mkdir(parents=True, exist_ok=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f18878ea",
   "metadata": {},
   "source": [
    "## Fig S4: BA structures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "f2eba968",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|████████████████████████████████████████████████████████| 4/4 [1:05:56<00:00, 989.19s/it]\n"
     ]
    }
   ],
   "source": [
    "N = 300\n",
    "M = [20, 40, 60, 80]\n",
    "\n",
    "BASs = []\n",
    "\n",
    "# generate structures\n",
    "for j, m in enumerate(tqdm(M)):\n",
    "\n",
    "    # generate BA graphs:\n",
    "    # A graph of N nodes is grown by attaching new nodes each with m edges\n",
    "    # that are preferentially attached to existing nodes with high degree.\n",
    "    barabasi_albert = nx.barabasi_albert_graph(N, m, seed=42)\n",
    "\n",
    "    # generate maximum simplicial complex\n",
    "    MSC = flag_complex_d2(barabasi_albert)\n",
    "\n",
    "    BASs.append(MSC)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "d6c8f011",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|███████████████████████████████████████████████████████████| 4/4 [02:26<00:00, 36.55s/it]\n"
     ]
    }
   ],
   "source": [
    "alphas = np.arange(0, 1.01, 0.05)\n",
    "\n",
    "lyaps_BASs = np.zeros((len(M), len(alphas), N))\n",
    "\n",
    "# compute Lyapunov exponents\n",
    "for j, S in enumerate(tqdm(BASs)):\n",
    "\n",
    "    for i, alpha in enumerate(alphas):\n",
    "\n",
    "        lyap_multi = compute_eigenvalues_multi(\n",
    "            S, orders=[1, 2], weights=[1 - alpha, alpha]\n",
    "        )\n",
    "\n",
    "        lyap_multi = np.sort(lyap_multi)[::-1]\n",
    "        lyaps_BASs[j, i, :] = lyap_multi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "f4d2cd4e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 340x235 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(3.4, 2.35))\n",
    "\n",
    "palette = sb.dark_palette(\"#69d\", reverse=True)\n",
    "sb.set_palette(palette)\n",
    "\n",
    "for i, m in enumerate(M):\n",
    "    ax.plot(alphas, lyaps_BASs[i, :, 1], \"o-\", label=f\"$m={m:.0f}$\", ms=5)\n",
    "\n",
    "ax.set_ylabel(r\"$\\lambda_2$\")\n",
    "ax.set_xlabel(r\"$\\alpha$\")\n",
    "\n",
    "ax.set_yticks([-0.0, -0.3, -0.6])\n",
    "ax.set_xticks([0, 0.5, 1])\n",
    "\n",
    "xvals = [0.15] * 4\n",
    "offsets = [0.045, -0.01, -0.049, -0.049]\n",
    "labelLines(\n",
    "    plt.gca().get_lines(), align=True, xvals=xvals, yoffsets=offsets, outline_width=5\n",
    ")\n",
    "\n",
    "sb.despine()\n",
    "\n",
    "fig_name = f\"figure_S4_MSC_barabasi_albert\"\n",
    "plt.savefig(f\"{fig_dir}{fig_name}.pdf\", dpi=250, bbox_inches=\"tight\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8126547",
   "metadata": {},
   "source": [
    "## Fig S5: WS structures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "7aac191f",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████████████████████████████████████████████████████| 4/4 [23:26<00:00, 351.74s/it]\n"
     ]
    }
   ],
   "source": [
    "N = 300  # Size of the graph\n",
    "M = [\n",
    "    30,\n",
    "    50,\n",
    "    70,\n",
    "    90,\n",
    "]  # Each node is joined with its m nearest neighbors in a ring topology\n",
    "p = 0.15  # The probability of rewiring each edge\n",
    "\n",
    "WSs = []\n",
    "\n",
    "# generate structures\n",
    "for j, m in enumerate(tqdm(M)):\n",
    "\n",
    "    # generate SW graphs\n",
    "    watts_strogatz = nx.watts_strogatz_graph(N, m, p)\n",
    "\n",
    "    # generate maximum simplicial complex\n",
    "    MSC = flag_complex_d2(watts_strogatz)\n",
    "\n",
    "    WSs.append(MSC)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "27f30efe",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|███████████████████████████████████████████████████████████| 4/4 [01:18<00:00, 19.71s/it]\n"
     ]
    }
   ],
   "source": [
    "alphas = np.arange(0, 1.01, 0.05)\n",
    "\n",
    "lyaps_WS = np.zeros((len(M), len(alphas), N))\n",
    "\n",
    "# compute Lyapunov exponents\n",
    "for j, S in enumerate(tqdm(WSs)):\n",
    "\n",
    "    for i, alpha in enumerate(alphas):\n",
    "\n",
    "        lyap_multi = compute_eigenvalues_multi(\n",
    "            S, orders=[1, 2], weights=[1 - alpha, alpha]\n",
    "        )\n",
    "\n",
    "        lyap_multi = np.sort(lyap_multi)[::-1]\n",
    "        lyaps_WS[j, i, :] = lyap_multi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "f103eb7b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 340x235 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(3.4, 2.35))\n",
    "\n",
    "palette = sb.dark_palette(\"#69d\", reverse=True)\n",
    "sb.set_palette(palette)\n",
    "\n",
    "for i, m in enumerate(M):\n",
    "    ax.plot(alphas, lyaps_WS[i, :, 1], \"o-\", label=f\"$m={m:.0f}$\", ms=5)\n",
    "\n",
    "ax.set_ylabel(r\"$\\lambda_2$\")\n",
    "ax.set_xlabel(r\"$\\alpha$\")\n",
    "\n",
    "ax.set_yticks([-0.0, -0.1, -0.2, -0.3])\n",
    "ax.set_xticks([0, 0.5, 1])\n",
    "\n",
    "xvals = [0.1] * 4\n",
    "labelLines(\n",
    "    plt.gca().get_lines(), align=True, xvals=xvals, yoffsets=0.019, outline_width=3\n",
    ")\n",
    "\n",
    "sb.despine()\n",
    "\n",
    "fig_name = f\"fig_S5_MSC_watts_strogatz\"\n",
    "plt.savefig(f\"{fig_dir}{fig_name}.pdf\", dpi=250, bbox_inches=\"tight\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "74a49c84",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "venv_xgi",
   "language": "python",
   "name": "venv_xgi"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.13"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": true
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}