{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "9ce609d5",
   "metadata": {},
   "source": [
    "# Basics\n"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    ".. admonition:: Definition\n",
    "\n",
    "   A hypergraph is a set of nodes and a collection of hyperedges, each connecting any number of nodes.\n"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    ".. admonition:: You will learn\n",
    "\n",
    "   Build a small hypergraph and use the core HGX API for inspection and basic measures.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Overview\n",
    "\n",
    "- Build a first hypergraph and inspect nodes, edges, and metadata.\n",
    "- Compute a few core measures to get comfortable with the API.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setup\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib as mpl\n",
    "\n",
    "mpl.rcParams.update({\n",
    "    \"figure.figsize\": (6, 4),\n",
    "    \"figure.dpi\": 120,\n",
    "    \"savefig.dpi\": 150,\n",
    "})\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d6d817d8",
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "sys.path.append(\"..\")\n",
    "\n",
    "from hypergraphx.generation.scale_free import scale_free_hypergraph\n",
    "from hypergraphx.linalg import *\n",
    "from hypergraphx.representations.projections import bipartite_projection, clique_projection\n",
    "from hypergraphx.generation.random import *\n",
    "from hypergraphx.readwrite.save import save_hypergraph\n",
    "from hypergraphx.readwrite.load import load_hypergraph\n",
    "from hypergraphx.viz.draw_hypergraph import draw_hypergraph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "edb8ec90",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hypergraph with 8 nodes and 5 edges.\n",
      "Distribution of hyperedge sizes: {2: 3, 4: 1, 3: 1}\n"
     ]
    }
   ],
   "source": [
    "H = Hypergraph([(1, 3), (1, 4), (1, 2), (5, 6, 7, 8), (1, 2, 3)])\n",
    "print(H)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "443ed5cc",
   "metadata": {},
   "outputs": [],
   "source": [
    "H = Hypergraph([(1, 3), (1, 4), (1, 2), (5, 6, 7, 8), (1, 2, 3)], weighted=True, weights=[1, 2, 3, 4, 5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c89cda8b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(1, 3), (1, 4), (1, 2), (5, 6, 7, 8), (1, 2, 3)]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H.get_edges()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "3574dd39",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3, 4, 5]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H.get_weights()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f023b14a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "((1, 3), 0)\n",
      "((1, 4), 1)\n",
      "((1, 2), 2)\n",
      "((5, 6, 7, 8), 3)\n",
      "((1, 2, 3), 4)\n"
     ]
    }
   ],
   "source": [
    "for edge in H:\n",
    "    print(edge)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "7a63549e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H.get_weight((1, 2, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "11ab1373",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H.get_weight((2, 3, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "c665439e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H.is_connected()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "22b04b9f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1440x840 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw_hypergraph(H)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "560c6cf8",
   "metadata": {},
   "outputs": [],
   "source": [
    "H.add_edge((1,5), weight=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "5cd23330",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1440x840 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw_hypergraph(H)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "2ab0a529",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H.is_connected()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "214e1d84",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H.is_uniform()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "787ddc90",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "print(H.check_edge((5, 6, 7, 8)))\n",
    "H.remove_edge((5, 6, 7, 8))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "3eead6ec",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(1, 3), (1, 4), (1, 2), (1, 2, 3), (1, 5)]\n",
      "[1, 2, 3, 5, 10]\n"
     ]
    }
   ],
   "source": [
    "print(H.get_edges())\n",
    "print(H.get_weights())\n",
    "H.remove_edges([(1,2,3), (1,3)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "512c9bd5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(1, 4), (1, 2), (1, 5)]\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "print(H.get_edges())\n",
    "print(H.is_uniform())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "8eb21d84",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(1, 4), (1, 2), (1, 5)]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H.get_edges()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "cb1d0321",
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'Hypergraph' object has no attribute 'add_attr_to_node_metadata'",
     "output_type": "error",
     "traceback": [
      "\u001b[31m---------------------------------------------------------------------------\u001b[39m",
      "\u001b[31mAttributeError\u001b[39m                            Traceback (most recent call last)",
      "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[20]\u001b[39m\u001b[32m, line 1\u001b[39m\n\u001b[32m----> \u001b[39m\u001b[32m1\u001b[39m \u001b[43mH\u001b[49m\u001b[43m.\u001b[49m\u001b[43madd_attr_to_node_metadata\u001b[49m(\u001b[32m1\u001b[39m, \u001b[33m'\u001b[39m\u001b[33mrole\u001b[39m\u001b[33m'\u001b[39m, \u001b[33m'\u001b[39m\u001b[33mstudent\u001b[39m\u001b[33m'\u001b[39m)\n",
      "\u001b[31mAttributeError\u001b[39m: 'Hypergraph' object has no attribute 'add_attr_to_node_metadata'"
     ]
    }
   ],
   "source": [
    "H.add_attr_to_node_metadata(1, 'role', 'student')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a6ce1a0b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1: {'role': 'student'}, 3: {}, 4: {}, 2: {}, 5: {}, 6: {}, 7: {}, 8: {}}"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H.get_nodes(metadata=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "88039218",
   "metadata": {},
   "outputs": [],
   "source": [
    "H.remove_node(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7d576e4e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{3: {}, 4: {}, 2: {}, 5: {}, 6: {}, 7: {}, 8: {}}"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H.get_nodes(metadata=True)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "hgx-installation",
   "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": "3.11.5"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 5
}