docs/tutorials/topology/core_decomposition.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Core decomposition"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook illustrates the $k$-core decomposition of graphs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.display import SVG"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-15T12:29:50.554431Z",
     "start_time": "2019-07-15T12:29:50.414075Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sknetwork.data import karate_club, painters\n",
    "from sknetwork.topology import CoreDecomposition\n",
    "from sknetwork.visualization import svg_graph, svg_digraph\n",
    "from sknetwork.utils import directed2undirected"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Graphs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-15T12:29:51.261957Z",
     "start_time": "2019-07-15T12:29:51.249107Z"
    }
   },
   "outputs": [],
   "source": [
    "graph = karate_club(metadata=True)\n",
    "adjacency = graph.adjacency\n",
    "position = graph.position"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "core = CoreDecomposition()\n",
    "labels = core.fit_transform(adjacency)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-15T12:29:55.341520Z",
     "start_time": "2019-07-15T12:29:55.026465Z"
    },
    "scrolled": true
   },
   "outputs": [
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      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "image = svg_graph(adjacency, position, scores=labels)\n",
    "SVG(image)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Directed graphs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-15T12:29:58.542147Z",
     "start_time": "2019-07-15T12:29:58.529699Z"
    }
   },
   "outputs": [],
   "source": [
    "graph = painters(metadata=True)\n",
    "adjacency = graph.adjacency\n",
    "names = graph.names\n",
    "position = graph.position"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "labels = core.fit_transform(directed2undirected(adjacency))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
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      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "image = svg_digraph(adjacency, position, names, scores=labels)\n",
    "SVG(image)"
   ]
  }
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