{
 "cells": [
  {
   "cell_type": "raw",
   "metadata": {
    "editable": true,
    "raw_mimetype": "text/restructuredtext",
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    ".. _user_guide_graph:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "# Graphs and Graph Routines"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The library only provides a few tools for graphs, related to algorithms for bandwith reduction, such as the calculation of pseudo peripheral nodes and rooted level structures."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `Graph` class is a subclass of the `Graph` class from `networkx`, with a few additions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sigmaepsilon.math.graph import Graph\n",
    "import networkx as nx\n",
    "\n",
    "grid = nx.grid_2d_graph(5, 5)  # 5x5 grid\n",
    "G = Graph(grid)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One of these additions is that it is possible to get the adjacency matrix of a graph directly, by calling the `adjacency_matrix` method of an instance. The method returns a Numba-jittable instance of the `csr_matrix` class from `sigmaepsilon.math.linalg`, hence making the graph instance itself sort of Numba-jittable as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Compressed Sparse Row sparse array of dtype 'int32'\n",
       "\twith 80 stored elements and shape (25, 25)>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G.adjacency_matrix()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `Graph` class in `sigmaepsilon.math.graph` is also equipped with methods for the calculation of pseudo peripheral nodes and rooted level structures."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([24,  0], dtype=int64)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G.pseudo_peripheral_nodes()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DictType[int64,array(int64, 1d, C)]<iv=None>({0: [0], 1: [1 5], 2: [ 2  6 10], 3: [ 3  7 11 15], 4: [ 4  8 12 16 20], 5: [ 9 13 17 21], 6: [14 18 22], 7: [19 23], 8: [24]})"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G.rooted_level_structure()"
   ]
  }
 ],
 "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": "3.10.11"
  },
  "vscode": {
   "interpreter": {
    "hash": "4e251a336b180e3c877fd4b81be72acfad98293ac2abcf90f00390a06765d313"
   }
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {},
    "version_major": 2,
    "version_minor": 0
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}