add new workbooks for mlp and graph measures and train-test split

Project: http://git-wip-us.apache.org/repos/asf/incubator-madlib-site/repo
Commit: 
http://git-wip-us.apache.org/repos/asf/incubator-madlib-site/commit/7fa3b796
Tree: http://git-wip-us.apache.org/repos/asf/incubator-madlib-site/tree/7fa3b796
Diff: http://git-wip-us.apache.org/repos/asf/incubator-madlib-site/diff/7fa3b796

Branch: refs/heads/asf-site
Commit: 7fa3b796519e4ae386102d8457a424532e3e3f03
Parents: d147759
Author: Frank McQuillan <fmcquil...@pivotal.io>
Authored: Mon Aug 21 13:15:56 2017 -0700
Committer: Frank McQuillan <fmcquil...@pivotal.io>
Committed: Mon Aug 21 13:15:56 2017 -0700

----------------------------------------------------------------------
 community-artifacts/Graph-measures-v1.ipynb   | 2532 ++++++++++++++++++++
 community-artifacts/Train-test-split-v1.ipynb | 1154 +++++++++
 community-artifacts/mlp-v1.ipynb              | 1525 ++++++++++++
 3 files changed, 5211 insertions(+)
----------------------------------------------------------------------


http://git-wip-us.apache.org/repos/asf/incubator-madlib-site/blob/7fa3b796/community-artifacts/Graph-measures-v1.ipynb
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diff --git a/community-artifacts/Graph-measures-v1.ipynb 
b/community-artifacts/Graph-measures-v1.ipynb
new file mode 100644
index 0000000..49e753f
--- /dev/null
+++ b/community-artifacts/Graph-measures-v1.ipynb
@@ -0,0 +1,2532 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Graph measures\n",
+    "\n",
+    "- Closeness\n",
+    "- Graph diameter\n",
+    "- Average path length\n",
+    "- In-out degree\n",
+    "\n",
+    "Graph measures were added in MADlib 1.12.  Some graph measures require a 
valid output from a prior APSP run - both the APSP table and the associated 
output summary table must be present."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      
"/Users/fmcquillan/anaconda/lib/python2.7/site-packages/IPython/config.py:13: 
ShimWarning: The `IPython.config` package has been deprecated. You should 
import from traitlets.config instead.\n",
+      "  \"You should import from traitlets.config instead.\", ShimWarning)\n",
+      
"/Users/fmcquillan/anaconda/lib/python2.7/site-packages/IPython/utils/traitlets.py:5:
 UserWarning: IPython.utils.traitlets has moved to a top-level traitlets 
package.\n",
+      "  warn(\"IPython.utils.traitlets has moved to a top-level traitlets 
package.\")\n"
+     ]
+    }
+   ],
+   "source": [
+    "%load_ext sql"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "u'Connected: gpdbchina@madlib'"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# Greenplum 4.3.10.0\n",
+    "%sql postgresql://gpdbchina@10.194.10.68:61000/madlib\n",
+    "        \n",
+    "# PostgreSQL local\n",
+    "#%sql postgresql://fmcquillan@localhost:5432/madlib\n",
+    "\n",
+    "# Greenplum 4.2.3.0\n",
+    "#%sql postgresql://gpdbchina@10.194.10.68:55000/madlib"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1 rows affected.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<table>\n",
+       "    <tr>\n",
+       "        <th>version</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>MADlib version: 1.12-dev, git revision: 
rel/v1.11-51-g69f7886, cmake configuration time: Fri Aug 18 16:30:51 UTC 2017, 
build type: Release, build system: Linux-2.6.18-238.27.1.el5.hotfix.bz516490, C 
compiler: gcc 4.4.0, C++ compiler: g++ 4.4.0</td>\n",
+       "    </tr>\n",
+       "</table>"
+      ],
+      "text/plain": [
+       "[(u'MADlib version: 1.12-dev, git revision: rel/v1.11-51-g69f7886, 
cmake configuration time: Fri Aug 18 16:30:51 UTC 2017, build type: Release, 
build system: Linux-2.6.18-238.27.1.el5.hotfix.bz516490, C compiler: gcc 4.4.0, 
C++ compiler: g++ 4.4.0',)]"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%sql select madlib.version();\n",
+    "#%sql select version();"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Closeness"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 1.  Create vertex and edge tables"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Done.\n",
+      "Done.\n",
+      "Done.\n",
+      "8 rows affected.\n",
+      "12 rows affected.\n",
+      "12 rows affected.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<table>\n",
+       "    <tr>\n",
+       "        <th>src_id</th>\n",
+       "        <th>dest_id</th>\n",
+       "        <th>edge_weight</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>1</td>\n",
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+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>4</td>\n",
+       "        <td>10.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>2</td>\n",
+       "        <td>2.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>3</td>\n",
+       "        <td>10.0</td>\n",
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+       "    <tr>\n",
+       "        <td>2</td>\n",
+       "        <td>3</td>\n",
+       "        <td>1.0</td>\n",
+       "    </tr>\n",
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+       "        <td>2</td>\n",
+       "        <td>5</td>\n",
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+       "        <td>2</td>\n",
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+       "        <td>0</td>\n",
+       "        <td>1.0</td>\n",
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+       "        <td>4</td>\n",
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+       "        <td>-2.0</td>\n",
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+       "        <td>6</td>\n",
+       "        <td>1.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>6</td>\n",
+       "        <td>7</td>\n",
+       "        <td>1.0</td>\n",
+       "    </tr>\n",
+       "</table>"
+      ],
+      "text/plain": [
+       "[(0, 1, 1.0),\n",
+       " (0, 2, 1.0),\n",
+       " (0, 4, 10.0),\n",
+       " (1, 2, 2.0),\n",
+       " (1, 3, 10.0),\n",
+       " (2, 3, 1.0),\n",
+       " (2, 5, 1.0),\n",
+       " (2, 6, 3.0),\n",
+       " (3, 0, 1.0),\n",
+       " (4, 0, -2.0),\n",
+       " (5, 6, 1.0),\n",
+       " (6, 7, 1.0)]"
+      ]
+     },
+     "execution_count": 18,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%%sql \n",
+    "DROP TABLE IF EXISTS vertex, edge;\n",
+    "\n",
+    "CREATE TABLE vertex(\n",
+    "        id INTEGER,\n",
+    "        name TEXT\n",
+    "        );\n",
+    "\n",
+    "CREATE TABLE edge(\n",
+    "        src_id INTEGER,\n",
+    "        dest_id INTEGER,\n",
+    "        edge_weight FLOAT8\n",
+    "        );\n",
+    "\n",
+    "INSERT INTO vertex VALUES\n",
+    "(0, 'A'),\n",
+    "(1, 'B'),\n",
+    "(2, 'C'),\n",
+    "(3, 'D'),\n",
+    "(4, 'E'),\n",
+    "(5, 'F'),\n",
+    "(6, 'G'),\n",
+    "(7, 'H');\n",
+    "\n",
+    "INSERT INTO edge VALUES\n",
+    "(0, 1, 1.0),\n",
+    "(0, 2, 1.0),\n",
+    "(0, 4, 10.0),\n",
+    "(1, 2, 2.0),\n",
+    "(1, 3, 10.0),\n",
+    "(2, 3, 1.0),\n",
+    "(2, 5, 1.0),\n",
+    "(2, 6, 3.0),\n",
+    "(3, 0, 1.0),\n",
+    "(4, 0, -2.0),\n",
+    "(5, 6, 1.0),\n",
+    "(6, 7, 1.0);\n",
+    "\n",
+    "SELECT * FROM edge ORDER BY src_id, dest_id;"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 2.  Calculate APSP"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Done.\n",
+      "1 rows affected.\n",
+      "64 rows affected.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<table>\n",
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+       "        <td>2.0</td>\n",
+       "        <td>6</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>6</td>\n",
+       "        <td>0</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>6</td>\n",
+       "        <td>1</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>6</td>\n",
+       "        <td>2</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>6</td>\n",
+       "        <td>3</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>6</td>\n",
+       "        <td>4</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>6</td>\n",
+       "        <td>5</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>6</td>\n",
+       "        <td>6</td>\n",
+       "        <td>0.0</td>\n",
+       "        <td>6</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>6</td>\n",
+       "        <td>7</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>7</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>7</td>\n",
+       "        <td>0</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>7</td>\n",
+       "        <td>1</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>7</td>\n",
+       "        <td>2</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>7</td>\n",
+       "        <td>3</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>7</td>\n",
+       "        <td>4</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>7</td>\n",
+       "        <td>5</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>7</td>\n",
+       "        <td>6</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>7</td>\n",
+       "        <td>7</td>\n",
+       "        <td>0.0</td>\n",
+       "        <td>7</td>\n",
+       "    </tr>\n",
+       "</table>"
+      ],
+      "text/plain": [
+       "[(0, 0, 0.0, 0),\n",
+       " (0, 1, 1.0, 1),\n",
+       " (0, 2, 1.0, 2),\n",
+       " (0, 3, 2.0, 2),\n",
+       " (0, 4, 10.0, 4),\n",
+       " (0, 5, 2.0, 2),\n",
+       " (0, 6, 3.0, 5),\n",
+       " (0, 7, 4.0, 6),\n",
+       " (1, 0, 4.0, 3),\n",
+       " (1, 1, 0.0, 1),\n",
+       " (1, 2, 2.0, 2),\n",
+       " (1, 3, 3.0, 2),\n",
+       " (1, 4, 14.0, 0),\n",
+       " (1, 5, 3.0, 2),\n",
+       " (1, 6, 4.0, 5),\n",
+       " (1, 7, 5.0, 6),\n",
+       " (2, 0, 2.0, 3),\n",
+       " (2, 1, 3.0, 0),\n",
+       " (2, 2, 0.0, 2),\n",
+       " (2, 3, 1.0, 3),\n",
+       " (2, 4, 12.0, 0),\n",
+       " (2, 5, 1.0, 5),\n",
+       " (2, 6, 2.0, 5),\n",
+       " (2, 7, 3.0, 6),\n",
+       " (3, 0, 1.0, 0),\n",
+       " (3, 1, 2.0, 0),\n",
+       " (3, 2, 2.0, 0),\n",
+       " (3, 3, 0.0, 3),\n",
+       " (3, 4, 11.0, 0),\n",
+       " (3, 5, 3.0, 2),\n",
+       " (3, 6, 4.0, 5),\n",
+       " (3, 7, 5.0, 6),\n",
+       " (4, 0, -2.0, 0),\n",
+       " (4, 1, -1.0, 0),\n",
+       " (4, 2, -1.0, 0),\n",
+       " (4, 3, 0.0, 2),\n",
+       " (4, 4, 0.0, 4),\n",
+       " (4, 5, 0.0, 2),\n",
+       " (4, 6, 1.0, 5),\n",
+       " (4, 7, 2.0, 6),\n",
+       " (5, 0, inf, None),\n",
+       " (5, 1, inf, None),\n",
+       " (5, 2, inf, None),\n",
+       " (5, 3, inf, None),\n",
+       " (5, 4, inf, None),\n",
+       " (5, 5, 0.0, 5),\n",
+       " (5, 6, 1.0, 6),\n",
+       " (5, 7, 2.0, 6),\n",
+       " (6, 0, inf, None),\n",
+       " (6, 1, inf, None),\n",
+       " (6, 2, inf, None),\n",
+       " (6, 3, inf, None),\n",
+       " (6, 4, inf, None),\n",
+       " (6, 5, inf, None),\n",
+       " (6, 6, 0.0, 6),\n",
+       " (6, 7, 1.0, 7),\n",
+       " (7, 0, inf, None),\n",
+       " (7, 1, inf, None),\n",
+       " (7, 2, inf, None),\n",
+       " (7, 3, inf, None),\n",
+       " (7, 4, inf, None),\n",
+       " (7, 5, inf, None),\n",
+       " (7, 6, inf, None),\n",
+       " (7, 7, 0.0, 7)]"
+      ]
+     },
+     "execution_count": 29,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%%sql\n",
+    "DROP TABLE IF EXISTS out_apsp, out_apsp_summary;\n",
+    "\n",
+    "SELECT madlib.graph_apsp('vertex',      -- Vertex table\n",
+    "                         'id',          -- Vertix id column (NULL means 
use default naming)\n",
+    "                         'edge',        -- Edge table\n",
+    "                         'src=src_id, dest=dest_id, 
weight=edge_weight',\n",
+    "                                        -- Edge arguments (NULL means use 
default naming)\n",
+    "                         'out_apsp');   -- Output table of shortest 
paths\n",
+    "\n",
+    "SELECT * FROM out_apsp ORDER BY src_id, dest_id;"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 3.  Compute the closeness measure for all nodes"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Done.\n",
+      "1 rows affected.\n",
+      "8 rows affected.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<table>\n",
+       "    <tr>\n",
+       "        <th>src_id</th>\n",
+       "        <th>inverse_sum_dist</th>\n",
+       "        <th>inverse_avg_dist</th>\n",
+       "        <th>sum_inverse_dist</th>\n",
+       "        <th>k_degree</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>0.0434782608696</td>\n",
+       "        <td>0.304347826087</td>\n",
+       "        <td>3.68333333333</td>\n",
+       "        <td>7</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>0.0285714285714</td>\n",
+       "        <td>0.2</td>\n",
+       "        <td>1.9380952381</td>\n",
+       "        <td>7</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>2</td>\n",
+       "        <td>0.0416666666667</td>\n",
+       "        <td>0.291666666667</td>\n",
+       "        <td>3.75</td>\n",
+       "        <td>7</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>3</td>\n",
+       "        <td>0.0357142857143</td>\n",
+       "        <td>0.25</td>\n",
+       "        <td>2.87424242424</td>\n",
+       "        <td>7</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>4</td>\n",
+       "        <td>-1.0</td>\n",
+       "        <td>-7.0</td>\n",
+       "        <td>-1.0</td>\n",
+       "        <td>7</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>5</td>\n",
+       "        <td>0.333333333333</td>\n",
+       "        <td>0.666666666667</td>\n",
+       "        <td>1.5</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>6</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>7</td>\n",
+       "        <td>None</td>\n",
+       "        <td>None</td>\n",
+       "        <td>0.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "</table>"
+      ],
+      "text/plain": [
+       "[(0, 0.0434782608695652, 0.304347826086957, 3.68333333333333, 7L),\n",
+       " (1, 0.0285714285714286, 0.2, 1.93809523809524, 7L),\n",
+       " (2, 0.0416666666666667, 0.291666666666667, 3.75, 7L),\n",
+       " (3, 0.0357142857142857, 0.25, 2.87424242424242, 7L),\n",
+       " (4, -1.0, -7.0, -1.0, 7L),\n",
+       " (5, 0.333333333333333, 0.666666666666667, 1.5, 2L),\n",
+       " (6, 1.0, 1.0, 1.0, 1L),\n",
+       " (7, None, None, 0.0, 0L)]"
+      ]
+     },
+     "execution_count": 20,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%%sql\n",
+    "DROP TABLE IF EXISTS out_closeness;\n",
+    "SELECT madlib.graph_closeness('out_apsp', 'out_closeness');\n",
+    "SELECT * FROM out_closeness ORDER BY src_id;"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 4.  Create a graph with 2 groups"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Done.\n",
+      "21 rows affected.\n",
+      "1 rows affected.\n",
+      "22 rows affected.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<table>\n",
+       "    <tr>\n",
+       "        <th>src_id</th>\n",
+       "        <th>dest_id</th>\n",
+       "        <th>edge_weight</th>\n",
+       "        <th>grp</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>1</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>2</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>4</td>\n",
+       "        <td>10.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>2</td>\n",
+       "        <td>2.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>3</td>\n",
+       "        <td>10.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>2</td>\n",
+       "        <td>3</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>2</td>\n",
+       "        <td>5</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>2</td>\n",
+       "        <td>6</td>\n",
+       "        <td>3.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>3</td>\n",
+       "        <td>0</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>4</td>\n",
+       "        <td>0</td>\n",
+       "        <td>-2.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>5</td>\n",
+       "        <td>6</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>6</td>\n",
+       "        <td>7</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>1</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>2</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>4</td>\n",
+       "        <td>10.0</td>\n",
+       "        <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>2</td>\n",
+       "        <td>2.0</td>\n",
+       "        <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>3</td>\n",
+       "        <td>10.0</td>\n",
+       "        <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>2</td>\n",
+       "        <td>3</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>2</td>\n",
+       "        <td>5</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>3</td>\n",
+       "        <td>0</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>4</td>\n",
+       "        <td>0</td>\n",
+       "        <td>-2.0</td>\n",
+       "        <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>4</td>\n",
+       "        <td>5</td>\n",
+       "        <td>-20.0</td>\n",
+       "        <td>1</td>\n",
+       "    </tr>\n",
+       "</table>"
+      ],
+      "text/plain": [
+       "[(0, 1, 1.0, 0),\n",
+       " (0, 2, 1.0, 0),\n",
+       " (0, 4, 10.0, 0),\n",
+       " (1, 2, 2.0, 0),\n",
+       " (1, 3, 10.0, 0),\n",
+       " (2, 3, 1.0, 0),\n",
+       " (2, 5, 1.0, 0),\n",
+       " (2, 6, 3.0, 0),\n",
+       " (3, 0, 1.0, 0),\n",
+       " (4, 0, -2.0, 0),\n",
+       " (5, 6, 1.0, 0),\n",
+       " (6, 7, 1.0, 0),\n",
+       " (0, 1, 1.0, 1),\n",
+       " (0, 2, 1.0, 1),\n",
+       " (0, 4, 10.0, 1),\n",
+       " (1, 2, 2.0, 1),\n",
+       " (1, 3, 10.0, 1),\n",
+       " (2, 3, 1.0, 1),\n",
+       " (2, 5, 1.0, 1),\n",
+       " (3, 0, 1.0, 1),\n",
+       " (4, 0, -2.0, 1),\n",
+       " (4, 5, -20.0, 1)]"
+      ]
+     },
+     "execution_count": 31,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%%sql \n",
+    "DROP TABLE IF EXISTS edge_gr;\n",
+    "\n",
+    "CREATE TABLE edge_gr AS\n",
+    "(\n",
+    "  SELECT *, 0 AS grp FROM edge\n",
+    "  UNION\n",
+    "  SELECT *, 1 AS grp FROM edge WHERE src_id < 6 AND dest_id < 6\n",
+    ");\n",
+    "\n",
+    "INSERT INTO edge_gr VALUES\n",
+    "(4,5,-20,1);\n",
+    "\n",
+    "SELECT * FROM edge_gr ORDER BY grp, src_id, dest_id;"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 5.  Find APSP for all groups"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Done.\n",
+      "1 rows affected.\n",
+      "100 rows affected.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<table>\n",
+       "    <tr>\n",
+       "        <th>grp</th>\n",
+       "        <th>src_id</th>\n",
+       "        <th>dest_id</th>\n",
+       "        <th>edge_weight</th>\n",
+       "        <th>parent</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>0</td>\n",
+       "        <td>0</td>\n",
+       "        <td>0.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>0</td>\n",
+       "        <td>1</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>0</td>\n",
+       "        <td>2</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>0</td>\n",
+       "        <td>3</td>\n",
+       "        <td>2.0</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>0</td>\n",
+       "        <td>4</td>\n",
+       "        <td>10.0</td>\n",
+       "        <td>4</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>0</td>\n",
+       "        <td>5</td>\n",
+       "        <td>2.0</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>0</td>\n",
+       "        <td>6</td>\n",
+       "        <td>3.0</td>\n",
+       "        <td>5</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>0</td>\n",
+       "        <td>7</td>\n",
+       "        <td>4.0</td>\n",
+       "        <td>6</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>1</td>\n",
+       "        <td>0</td>\n",
+       "        <td>4.0</td>\n",
+       "        <td>3</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>1</td>\n",
+       "        <td>1</td>\n",
+       "        <td>0.0</td>\n",
+       "        <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>1</td>\n",
+       "        <td>2</td>\n",
+       "        <td>2.0</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>1</td>\n",
+       "        <td>3</td>\n",
+       "        <td>3.0</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>1</td>\n",
+       "        <td>4</td>\n",
+       "        <td>14.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>1</td>\n",
+       "        <td>5</td>\n",
+       "        <td>3.0</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>1</td>\n",
+       "        <td>6</td>\n",
+       "        <td>4.0</td>\n",
+       "        <td>5</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>1</td>\n",
+       "        <td>7</td>\n",
+       "        <td>5.0</td>\n",
+       "        <td>6</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>2</td>\n",
+       "        <td>0</td>\n",
+       "        <td>2.0</td>\n",
+       "        <td>3</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>2</td>\n",
+       "        <td>1</td>\n",
+       "        <td>3.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>2</td>\n",
+       "        <td>2</td>\n",
+       "        <td>0.0</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>2</td>\n",
+       "        <td>3</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>3</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>2</td>\n",
+       "        <td>4</td>\n",
+       "        <td>12.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>2</td>\n",
+       "        <td>5</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>5</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>2</td>\n",
+       "        <td>6</td>\n",
+       "        <td>2.0</td>\n",
+       "        <td>5</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>2</td>\n",
+       "        <td>7</td>\n",
+       "        <td>3.0</td>\n",
+       "        <td>6</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>3</td>\n",
+       "        <td>0</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>3</td>\n",
+       "        <td>1</td>\n",
+       "        <td>2.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>3</td>\n",
+       "        <td>2</td>\n",
+       "        <td>2.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>3</td>\n",
+       "        <td>3</td>\n",
+       "        <td>0.0</td>\n",
+       "        <td>3</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>3</td>\n",
+       "        <td>4</td>\n",
+       "        <td>11.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>3</td>\n",
+       "        <td>5</td>\n",
+       "        <td>3.0</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>3</td>\n",
+       "        <td>6</td>\n",
+       "        <td>4.0</td>\n",
+       "        <td>5</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>3</td>\n",
+       "        <td>7</td>\n",
+       "        <td>5.0</td>\n",
+       "        <td>6</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>4</td>\n",
+       "        <td>0</td>\n",
+       "        <td>-2.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>4</td>\n",
+       "        <td>1</td>\n",
+       "        <td>-1.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>4</td>\n",
+       "        <td>2</td>\n",
+       "        <td>-1.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>4</td>\n",
+       "        <td>3</td>\n",
+       "        <td>0.0</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>4</td>\n",
+       "        <td>4</td>\n",
+       "        <td>0.0</td>\n",
+       "        <td>4</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>4</td>\n",
+       "        <td>5</td>\n",
+       "        <td>0.0</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>4</td>\n",
+       "        <td>6</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>5</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>4</td>\n",
+       "        <td>7</td>\n",
+       "        <td>2.0</td>\n",
+       "        <td>6</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>5</td>\n",
+       "        <td>0</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>5</td>\n",
+       "        <td>1</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>5</td>\n",
+       "        <td>2</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>5</td>\n",
+       "        <td>3</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>5</td>\n",
+       "        <td>4</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>5</td>\n",
+       "        <td>5</td>\n",
+       "        <td>0.0</td>\n",
+       "        <td>5</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>5</td>\n",
+       "        <td>6</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>6</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>5</td>\n",
+       "        <td>7</td>\n",
+       "        <td>2.0</td>\n",
+       "        <td>6</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>6</td>\n",
+       "        <td>0</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>6</td>\n",
+       "        <td>1</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>6</td>\n",
+       "        <td>2</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>6</td>\n",
+       "        <td>3</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>6</td>\n",
+       "        <td>4</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>6</td>\n",
+       "        <td>5</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>6</td>\n",
+       "        <td>6</td>\n",
+       "        <td>0.0</td>\n",
+       "        <td>6</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>6</td>\n",
+       "        <td>7</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>7</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>7</td>\n",
+       "        <td>0</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>7</td>\n",
+       "        <td>1</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>7</td>\n",
+       "        <td>2</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>7</td>\n",
+       "        <td>3</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>7</td>\n",
+       "        <td>4</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>7</td>\n",
+       "        <td>5</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>7</td>\n",
+       "        <td>6</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>7</td>\n",
+       "        <td>7</td>\n",
+       "        <td>0.0</td>\n",
+       "        <td>7</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>0</td>\n",
+       "        <td>0</td>\n",
+       "        <td>0.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>0</td>\n",
+       "        <td>1</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>0</td>\n",
+       "        <td>2</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>0</td>\n",
+       "        <td>3</td>\n",
+       "        <td>2.0</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>0</td>\n",
+       "        <td>4</td>\n",
+       "        <td>10.0</td>\n",
+       "        <td>4</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>0</td>\n",
+       "        <td>5</td>\n",
+       "        <td>-10.0</td>\n",
+       "        <td>4</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>1</td>\n",
+       "        <td>0</td>\n",
+       "        <td>4.0</td>\n",
+       "        <td>3</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>1</td>\n",
+       "        <td>1</td>\n",
+       "        <td>0.0</td>\n",
+       "        <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>1</td>\n",
+       "        <td>2</td>\n",
+       "        <td>2.0</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>1</td>\n",
+       "        <td>3</td>\n",
+       "        <td>3.0</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>1</td>\n",
+       "        <td>4</td>\n",
+       "        <td>14.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>1</td>\n",
+       "        <td>5</td>\n",
+       "        <td>-6.0</td>\n",
+       "        <td>4</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>2</td>\n",
+       "        <td>0</td>\n",
+       "        <td>2.0</td>\n",
+       "        <td>3</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>2</td>\n",
+       "        <td>1</td>\n",
+       "        <td>3.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>2</td>\n",
+       "        <td>2</td>\n",
+       "        <td>0.0</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>2</td>\n",
+       "        <td>3</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>3</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>2</td>\n",
+       "        <td>4</td>\n",
+       "        <td>12.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>2</td>\n",
+       "        <td>5</td>\n",
+       "        <td>-8.0</td>\n",
+       "        <td>4</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>3</td>\n",
+       "        <td>0</td>\n",
+       "        <td>1.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>3</td>\n",
+       "        <td>1</td>\n",
+       "        <td>2.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>3</td>\n",
+       "        <td>2</td>\n",
+       "        <td>2.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>3</td>\n",
+       "        <td>3</td>\n",
+       "        <td>0.0</td>\n",
+       "        <td>3</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>3</td>\n",
+       "        <td>4</td>\n",
+       "        <td>11.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>3</td>\n",
+       "        <td>5</td>\n",
+       "        <td>-9.0</td>\n",
+       "        <td>4</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>4</td>\n",
+       "        <td>0</td>\n",
+       "        <td>-2.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>4</td>\n",
+       "        <td>1</td>\n",
+       "        <td>-1.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>4</td>\n",
+       "        <td>2</td>\n",
+       "        <td>-1.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>4</td>\n",
+       "        <td>3</td>\n",
+       "        <td>0.0</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>4</td>\n",
+       "        <td>4</td>\n",
+       "        <td>0.0</td>\n",
+       "        <td>4</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>4</td>\n",
+       "        <td>5</td>\n",
+       "        <td>-20.0</td>\n",
+       "        <td>5</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>5</td>\n",
+       "        <td>0</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>5</td>\n",
+       "        <td>1</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>5</td>\n",
+       "        <td>2</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>5</td>\n",
+       "        <td>3</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>5</td>\n",
+       "        <td>4</td>\n",
+       "        <td>inf</td>\n",
+       "        <td>None</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>5</td>\n",
+       "        <td>5</td>\n",
+       "        <td>0.0</td>\n",
+       "        <td>5</td>\n",
+       "    </tr>\n",
+       "</table>"
+      ],
+      "text/plain": [
+       "[(0, 0, 0, 0.0, 0),\n",
+       " (0, 0, 1, 1.0, 1),\n",
+       " (0, 0, 2, 1.0, 2),\n",
+       " (0, 0, 3, 2.0, 2),\n",
+       " (0, 0, 4, 10.0, 4),\n",
+       " (0, 0, 5, 2.0, 2),\n",
+       " (0, 0, 6, 3.0, 5),\n",
+       " (0, 0, 7, 4.0, 6),\n",
+       " (0, 1, 0, 4.0, 3),\n",
+       " (0, 1, 1, 0.0, 1),\n",
+       " (0, 1, 2, 2.0, 2),\n",
+       " (0, 1, 3, 3.0, 2),\n",
+       " (0, 1, 4, 14.0, 0),\n",
+       " (0, 1, 5, 3.0, 2),\n",
+       " (0, 1, 6, 4.0, 5),\n",
+       " (0, 1, 7, 5.0, 6),\n",
+       " (0, 2, 0, 2.0, 3),\n",
+       " (0, 2, 1, 3.0, 0),\n",
+       " (0, 2, 2, 0.0, 2),\n",
+       " (0, 2, 3, 1.0, 3),\n",
+       " (0, 2, 4, 12.0, 0),\n",
+       " (0, 2, 5, 1.0, 5),\n",
+       " (0, 2, 6, 2.0, 5),\n",
+       " (0, 2, 7, 3.0, 6),\n",
+       " (0, 3, 0, 1.0, 0),\n",
+       " (0, 3, 1, 2.0, 0),\n",
+       " (0, 3, 2, 2.0, 0),\n",
+       " (0, 3, 3, 0.0, 3),\n",
+       " (0, 3, 4, 11.0, 0),\n",
+       " (0, 3, 5, 3.0, 2),\n",
+       " (0, 3, 6, 4.0, 5),\n",
+       " (0, 3, 7, 5.0, 6),\n",
+       " (0, 4, 0, -2.0, 0),\n",
+       " (0, 4, 1, -1.0, 0),\n",
+       " (0, 4, 2, -1.0, 0),\n",
+       " (0, 4, 3, 0.0, 2),\n",
+       " (0, 4, 4, 0.0, 4),\n",
+       " (0, 4, 5, 0.0, 2),\n",
+       " (0, 4, 6, 1.0, 5),\n",
+       " (0, 4, 7, 2.0, 6),\n",
+       " (0, 5, 0, inf, None),\n",
+       " (0, 5, 1, inf, None),\n",
+       " (0, 5, 2, inf, None),\n",
+       " (0, 5, 3, inf, None),\n",
+       " (0, 5, 4, inf, None),\n",
+       " (0, 5, 5, 0.0, 5),\n",
+       " (0, 5, 6, 1.0, 6),\n",
+       " (0, 5, 7, 2.0, 6),\n",
+       " (0, 6, 0, inf, None),\n",
+       " (0, 6, 1, inf, None),\n",
+       " (0, 6, 2, inf, None),\n",
+       " (0, 6, 3, inf, None),\n",
+       " (0, 6, 4, inf, None),\n",
+       " (0, 6, 5, inf, None),\n",
+       " (0, 6, 6, 0.0, 6),\n",
+       " (0, 6, 7, 1.0, 7),\n",
+       " (0, 7, 0, inf, None),\n",
+       " (0, 7, 1, inf, None),\n",
+       " (0, 7, 2, inf, None),\n",
+       " (0, 7, 3, inf, None),\n",
+       " (0, 7, 4, inf, None),\n",
+       " (0, 7, 5, inf, None),\n",
+       " (0, 7, 6, inf, None),\n",
+       " (0, 7, 7, 0.0, 7),\n",
+       " (1, 0, 0, 0.0, 0),\n",
+       " (1, 0, 1, 1.0, 1),\n",
+       " (1, 0, 2, 1.0, 2),\n",
+       " (1, 0, 3, 2.0, 2),\n",
+       " (1, 0, 4, 10.0, 4),\n",
+       " (1, 0, 5, -10.0, 4),\n",
+       " (1, 1, 0, 4.0, 3),\n",
+       " (1, 1, 1, 0.0, 1),\n",
+       " (1, 1, 2, 2.0, 2),\n",
+       " (1, 1, 3, 3.0, 2),\n",
+       " (1, 1, 4, 14.0, 0),\n",
+       " (1, 1, 5, -6.0, 4),\n",
+       " (1, 2, 0, 2.0, 3),\n",
+       " (1, 2, 1, 3.0, 0),\n",
+       " (1, 2, 2, 0.0, 2),\n",
+       " (1, 2, 3, 1.0, 3),\n",
+       " (1, 2, 4, 12.0, 0),\n",
+       " (1, 2, 5, -8.0, 4),\n",
+       " (1, 3, 0, 1.0, 0),\n",
+       " (1, 3, 1, 2.0, 0),\n",
+       " (1, 3, 2, 2.0, 0),\n",
+       " (1, 3, 3, 0.0, 3),\n",
+       " (1, 3, 4, 11.0, 0),\n",
+       " (1, 3, 5, -9.0, 4),\n",
+       " (1, 4, 0, -2.0, 0),\n",
+       " (1, 4, 1, -1.0, 0),\n",
+       " (1, 4, 2, -1.0, 0),\n",
+       " (1, 4, 3, 0.0, 2),\n",
+       " (1, 4, 4, 0.0, 4),\n",
+       " (1, 4, 5, -20.0, 5),\n",
+       " (1, 5, 0, inf, None),\n",
+       " (1, 5, 1, inf, None),\n",
+       " (1, 5, 2, inf, None),\n",
+       " (1, 5, 3, inf, None),\n",
+       " (1, 5, 4, inf, None),\n",
+       " (1, 5, 5, 0.0, 5)]"
+      ]
+     },
+     "execution_count": 32,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%%sql\n",
+    "DROP TABLE IF EXISTS out_gr, out_gr_summary;\n",
+    "\n",
+    "SELECT madlib.graph_apsp(\n",
+    "                         'vertex',      -- Vertex table\n",
+    "                         NULL,          -- Vertex id column (NULL means 
use default naming)\n",
+    "                         'edge_gr',     -- Edge table\n",
+    "                         'src=src_id, dest=dest_id, 
weight=edge_weight',\n",
+    "                         'out_gr',      -- Output table of shortest 
paths\n",
+    "                         'grp'          -- Grouping columns\n",
+    ");\n",
+    "\n",
+    "SELECT * FROM out_gr ORDER BY grp, src_id, dest_id;"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 6. Compute closeness measure for vertex 0 to vertex 5 in every group"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Done.\n",
+      "1 rows affected.\n",
+      "12 rows affected.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<table>\n",
+       "    <tr>\n",
+       "        <th>grp</th>\n",
+       "        <th>src_id</th>\n",
+       "        <th>inverse_sum_dist</th>\n",
+       "        <th>inverse_avg_dist</th>\n",
+       "        <th>sum_inverse_dist</th>\n",
+       "        <th>k_degree</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>0</td>\n",
+       "        <td>0.0434782608696</td>\n",
+       "        <td>0.304347826087</td>\n",
+       "        <td>3.68333333333</td>\n",
+       "        <td>7</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>1</td>\n",
+       "        <td>0.0285714285714</td>\n",
+       "        <td>0.2</td>\n",
+       "        <td>1.9380952381</td>\n",
+       "        <td>7</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>2</td>\n",
+       "        <td>0.0416666666667</td>\n",
+       "        <td>0.291666666667</td>\n",
+       "        <td>3.75</td>\n",
+       "        <td>7</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>3</td>\n",
+       "        <td>0.0357142857143</td>\n",
+       "        <td>0.25</td>\n",
+       "        <td>2.87424242424</td>\n",
+       "        <td>7</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>4</td>\n",
+       "        <td>-1.0</td>\n",
+       "        <td>-7.0</td>\n",
+       "        <td>-1.0</td>\n",
+       "        <td>7</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>5</td>\n",
+       "        <td>0.333333333333</td>\n",
+       "        <td>0.666666666667</td>\n",
+       "        <td>1.5</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>0</td>\n",
+       "        <td>0.25</td>\n",
+       "        <td>1.25</td>\n",
+       "        <td>2.5</td>\n",
+       "        <td>5</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>1</td>\n",
+       "        <td>0.0588235294118</td>\n",
+       "        <td>0.294117647059</td>\n",
+       "        <td>0.988095238095</td>\n",
+       "        <td>5</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>2</td>\n",
+       "        <td>0.1</td>\n",
+       "        <td>0.5</td>\n",
+       "        <td>1.79166666667</td>\n",
+       "        <td>5</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>3</td>\n",
+       "        <td>0.142857142857</td>\n",
+       "        <td>0.714285714286</td>\n",
+       "        <td>1.9797979798</td>\n",
+       "        <td>5</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>4</td>\n",
+       "        <td>-0.0416666666667</td>\n",
+       "        <td>-0.208333333333</td>\n",
+       "        <td>-2.55</td>\n",
+       "        <td>5</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>5</td>\n",
+       "        <td>None</td>\n",
+       "        <td>None</td>\n",
+       "        <td>0.0</td>\n",
+       "        <td>0</td>\n",
+       "    </tr>\n",
+       "</table>"
+      ],
+      "text/plain": [
+       "[(0, 0, 0.0434782608695652, 0.304347826086957, 3.68333333333333, 
7L),\n",
+       " (0, 1, 0.0285714285714286, 0.2, 1.93809523809524, 7L),\n",
+       " (0, 2, 0.0416666666666667, 0.291666666666667, 3.75, 7L),\n",
+       " (0, 3, 0.0357142857142857, 0.25, 2.87424242424242, 7L),\n",
+       " (0, 4, -1.0, -7.0, -1.0, 7L),\n",
+       " (0, 5, 0.333333333333333, 0.666666666666667, 1.5, 2L),\n",
+       " (1, 0, 0.25, 1.25, 2.5, 5L),\n",
+       " (1, 1, 0.0588235294117647, 0.294117647058824, 0.988095238095238, 
5L),\n",
+       " (1, 2, 0.1, 0.5, 1.79166666666667, 5L),\n",
+       " (1, 3, 0.142857142857143, 0.714285714285714, 1.97979797979798, 
5L),\n",
+       " (1, 4, -0.0416666666666667, -0.208333333333333, -2.55, 5L),\n",
+       " (1, 5, None, None, 0.0, 0L)]"
+      ]
+     },
+     "execution_count": 24,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%%sql\n",
+    "DROP TABLE IF EXISTS out_gr_closeness;\n",
+    "\n",
+    "SELECT madlib.graph_closeness(\n",
+    "    'out_gr', \n",
+    "    'out_gr_closeness', \n",
+    "    'src_id >= 0 and src_id <=5');\n",
+    "\n",
+    "SELECT * FROM out_gr_closeness ORDER BY grp, src_id;"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#  Graph Diameter\n",
+    "Use the same graph and APSP output from above."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Done.\n",
+      "1 rows affected.\n",
+      "1 rows affected.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<table>\n",
+       "    <tr>\n",
+       "        <th>diameter</th>\n",
+       "        <th>diameter_end_vertices</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>14.0</td>\n",
+       "        <td>[[1, 4]]</td>\n",
+       "    </tr>\n",
+       "</table>"
+      ],
+      "text/plain": [
+       "[(14.0, [[1, 4]])]"
+      ]
+     },
+     "execution_count": 26,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%%sql\n",
+    "DROP TABLE IF EXISTS out_diameter;\n",
+    "SELECT madlib.graph_diameter('out_apsp', 'out_diameter');\n",
+    "SELECT * FROM out_diameter;"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "For grouping, use the same graph and APSP output with grouping from 
above."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Done.\n",
+      "1 rows affected.\n",
+      "2 rows affected.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<table>\n",
+       "    <tr>\n",
+       "        <th>grp</th>\n",
+       "        <th>diameter</th>\n",
+       "        <th>diameter_end_vertices</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>14.0</td>\n",
+       "        <td>[[1, 4]]</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>14.0</td>\n",
+       "        <td>[[1, 4]]</td>\n",
+       "    </tr>\n",
+       "</table>"
+      ],
+      "text/plain": [
+       "[(0, 14.0, [[1, 4]]), (1, 14.0, [[1, 4]])]"
+      ]
+     },
+     "execution_count": 28,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%%sql\n",
+    "DROP TABLE IF EXISTS out_gr_path;\n",
+    "SELECT madlib.graph_diameter('out_gr', 'out_gr_diameter');\n",
+    "SELECT * FROM out_gr_diameter ORDER BY grp;"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#  Average Path Length\n",
+    "Use the same graph and APSP output from above."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 35,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Done.\n",
+      "1 rows affected.\n",
+      "1 rows affected.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<table>\n",
+       "    <tr>\n",
+       "        <th>avg_path_length</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>2.01785714286</td>\n",
+       "    </tr>\n",
+       "</table>"
+      ],
+      "text/plain": [
+       "[(2.01785714285714,)]"
+      ]
+     },
+     "execution_count": 35,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%%sql\n",
+    "DROP TABLE IF EXISTS out_avg_path_length;\n",
+    "SELECT madlib.graph_avg_path_length('out_apsp', 
'out_avg_path_length');\n",
+    "SELECT * FROM out_avg_path_length;"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "For grouping, use the same graph and APSP output with grouping from 
above."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Done.\n",
+      "1 rows affected.\n",
+      "2 rows affected.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<table>\n",
+       "    <tr>\n",
+       "        <th>grp</th>\n",
+       "        <th>avg_path_length</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>2.01785714286</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>0.466666666667</td>\n",
+       "    </tr>\n",
+       "</table>"
+      ],
+      "text/plain": [
+       "[(0, 2.01785714285714), (1, 0.466666666666667)]"
+      ]
+     },
+     "execution_count": 37,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%%sql\n",
+    "DROP TABLE IF EXISTS out_gr_path;\n",
+    "SELECT madlib.graph_avg_path_length('out_gr', 'out_gr_path');\n",
+    "SELECT * FROM out_gr_path ORDER BY grp;"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#  In-Out Degree\n",
+    "Use the same graph and APSP output from above."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Done.\n",
+      "1 rows affected.\n",
+      "7 rows affected.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<table>\n",
+       "    <tr>\n",
+       "        <th>id</th>\n",
+       "        <th>indegree</th>\n",
+       "        <th>outdegree</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>2</td>\n",
+       "        <td>3</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>1</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>2</td>\n",
+       "        <td>2</td>\n",
+       "        <td>3</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>3</td>\n",
+       "        <td>2</td>\n",
+       "        <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>4</td>\n",
+       "        <td>1</td>\n",
+       "        <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>5</td>\n",
+       "        <td>1</td>\n",
+       "        <td>1</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>6</td>\n",
+       "        <td>2</td>\n",
+       "        <td>1</td>\n",
+       "    </tr>\n",
+       "</table>"
+      ],
+      "text/plain": [
+       "[(0, 2L, 3L),\n",
+       " (1, 1L, 2L),\n",
+       " (2, 2L, 3L),\n",
+       " (3, 2L, 1L),\n",
+       " (4, 1L, 1L),\n",
+       " (5, 1L, 1L),\n",
+       " (6, 2L, 1L)]"
+      ]
+     },
+     "execution_count": 39,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%%sql\n",
+    "DROP TABLE IF EXISTS degrees;\n",
+    "\n",
+    "SELECT madlib.graph_vertex_degrees(\n",
+    "    'vertex',      -- Vertex table\n",
+    "    'id',          -- Vertix id column (NULL means use default naming)\n",
+    "    'edge',        -- Edge table\n",
+    "    'src=src_id, dest=dest_id, weight=edge_weight',\n",
+    "    'degrees');    -- Output table of shortest paths\n",
+    "\n",
+    "SELECT * FROM degrees ORDER BY id;"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "For grouping, use the same graph with grouping from above."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 42,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Done.\n",
+      "1 rows affected.\n",
+      "4 rows affected.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<table>\n",
+       "    <tr>\n",
+       "        <th>grp</th>\n",
+       "        <th>id</th>\n",
+       "        <th>indegree</th>\n",
+       "        <th>outdegree</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>0</td>\n",
+       "        <td>2</td>\n",
+       "        <td>3</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>0</td>\n",
+       "        <td>1</td>\n",
+       "        <td>1</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>0</td>\n",
+       "        <td>2</td>\n",
+       "        <td>3</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "        <td>1</td>\n",
+       "        <td>1</td>\n",
+       "        <td>1</td>\n",
+       "        <td>2</td>\n",
+       "    </tr>\n",
+       "</table>"
+      ],
+      "text/plain": [
+       "[(0, 0, 2L, 3L), (0, 1, 1L, 2L), (1, 0, 2L, 3L), (1, 1, 1L, 2L)]"
+      ]
+     },
+     "execution_count": 42,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%%sql \n",
+    "DROP TABLE IF EXISTS out_gr;\n",
+    "\n",
+    "SELECT madlib.graph_vertex_degrees(\n",
+    "    'vertex',      -- Vertex table\n",
+    "    NULL,          -- Vertex id column (NULL means use default naming)\n",
+    "    'edge_gr',     -- Edge table\n",
+    "    'src=src_id, dest=dest_id, weight=edge_weight',\n",
+    "    'out_gr',      -- Output table of shortest paths\n",
+    "    'grp'          -- Grouping columns\n",
+    ");\n",
+    "\n",
+    "SELECT * FROM out_gr WHERE id < 2 ORDER BY grp, id;"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 2",
+   "language": "python",
+   "name": "python2"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.12"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 1
+}

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