A.09_git_explore.ipynb

{
 "cells": [
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "---\n",
    "description: This is appendix for chapter [`09_git.ipynb`](09_git.ipynb)\n",
    "output-file: a.09_git_explore.html\n",
    "title: Exploring extraction of commit graphs from Git repositories, and examining\n",
    "  their shape and stats\n",
    "\n",
    "---\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#| output: false\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Necessary imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# creating graphs in Python\n",
    "import networkx as nx\n",
    "# calling git commands\n",
    "import subprocess\n",
    "# checking for existence of paths, and manipulating paths\n",
    "from pathlib import Path"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cloning git.git repository, and extracting and saving the commit graph"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Why it is important to use sparse clone - it is much faster, and takes up less space.  For example for git.git repository we have the following (all times are wall time, and subject to interference from other CPU load):\n",
    "- full clone: 54s\n",
    "- mirror: 1min 19s\n",
    "- sparse: 14.9s - 19.4s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Prepare the directory to store repositories (note: `mkdir -d <directory>` should show no error if `<directory>` exists, but it is not portable).\n",
    "\n",
    "Clone example repository (for exploration).  Might give errors if repository already exists."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create the directory to store cloned repositories, if it does not exist\n",
    "Path(\"repos\").mkdir(exist_ok=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 1.05 s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "fatal: destination path 'git.git' already exists and is not an empty directory.\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "!git -C repos clone --mirror --filter=tree:0 --quiet https://github.com/git/git.git"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Extract the history of the project"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create the directory to store datasets\n",
    "Path(\"datasets\").mkdir(exist_ok=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 6.81 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "!git -C repos/git.git log --format=\"%h %p\" --topo-order --branches >datasets/git-commit_graph.adjlist.txt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It takes a few seconds on a laptop with HDD to extract the commit graph (for all branches), storing results in a `git-commit_graph.adjlist.txt` text file in the adjacent list format in `datasets/` subdirectory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 663 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "graph_git = nx.read_adjlist(\"datasets/git-commit_graph.adjlist.txt\", create_using=nx.DiGraph)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It takes less than a second to create NetworkX graph for a commit graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "commit-graph of git repository graph has 63829 nodes and 79664 edges\n",
      "is directed:   True\n",
      "is DAG:        True\n",
      "example nodes: ['836aadd78', 'a93475d10', '55fce44a3', '6d9d59c31', '084bd2a9a']\n"
     ]
    }
   ],
   "source": [
    "print('commit-graph of git repository graph has {} nodes and {} edges'.format(\n",
    "      graph_git.number_of_nodes(),\n",
    "      graph_git.number_of_edges()))\n",
    "print('is directed:   {}'.format(graph_git.is_directed()))\n",
    "print('is DAG:        {}'.format(nx.is_directed_acyclic_graph(graph_git)))\n",
    "print('example nodes: {}'.format(list(graph_git.nodes)[:5]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "403 ms ± 32 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "# compress\n",
    "%timeit nx.write_adjlist(graph_git, 'datasets/git-commit_graph.adjlist.txt.gz')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It takes around 0.6-0.8 seconds to write it back gzip-compressed in the adjacency list format as `git-commit_graph.adjlist.txt.gz`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Testing different graph output formats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#%%time\n",
    "#nx.write_graph6(graph_git, 'datasets/git-commit_graph.g6')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It turns out that the [graph6 / sparse6 format](https://networkx.org/documentation/stable/reference/readwrite/sparsegraph6.html)\n",
    "is not a good choice for storing the commit graph for the following reasons:\n",
    "- NetworkX does not support digraph6 format; neither `write_graph6` not `write_sparse6` are implemented for directed graphs\n",
    "- the [digraph6 format](http://users.cecs.anu.edu.au/~bdm/data/formats.txt) is dense graph format, storing the encoded adjacency matrix; there is no disparse6 or digraph6sparse format\n",
    "- SparseGraph6 formats do not store node/vertex names, which might be needed for future computations or visualizations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pickle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "edgelist.txt:             Wall time: 244 ms\n",
      "multiline_adjlist.txt:    Wall time: 186 ms\n",
      "edgelist.txt.gz:          Wall time: 819 ms\n",
      "multiline_adjlist.txt.gz: Wall time: 1.06 s\n",
      "gexf.gz:                  Wall time: 5.34 s\n",
      "graphml.gz:               Wall time: 5.01 s\n",
      "pajek.gz:                 Wall time: 3.14 s\n"
     ]
    }
   ],
   "source": [
    "print('edgelist.txt:            ', end=' ', flush=True)\n",
    "%time nx.write_edgelist(graph_git, 'datasets/git-commit_graph.edgelist.txt')\n",
    "print('multiline_adjlist.txt:   ', end=' ', flush=True)\n",
    "%time nx.write_multiline_adjlist(graph_git, 'datasets/git-commit_graph.multiline_adjlist.txt')\n",
    "print('edgelist.txt.gz:         ', end=' ', flush=True)\n",
    "%time nx.write_edgelist(graph_git, 'datasets/git-commit_graph.edgelist.txt.gz')\n",
    "print('multiline_adjlist.txt.gz:', end=' ', flush=True)\n",
    "%time nx.write_multiline_adjlist(graph_git, 'datasets/git-commit_graph.multiline_adjlist.txt.gz')\n",
    "print('gexf.gz:                 ', end=' ', flush=True)\n",
    "%time nx.write_gexf(graph_git, 'datasets/git-commit_graph.gexf.gz')\n",
    "print('graphml.gz:              ', end=' ', flush=True)\n",
    "%time nx.write_graphml(graph_git, 'datasets/git-commit_graph.graphml.gz')\n",
    "print('pajek.gz:                ', end=' ', flush=True)\n",
    "%time nx.write_pajek(graph_git, 'datasets/git-commit_graph.pajek.gz')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gpickle.gz:               "
     ]
    }
   ],
   "source": [
    "#print('gpickle.gz:              ', end=' ', flush=True)\n",
    "#%time nx.write_gpickle(graph_git, 'datasets/git-commit_graph.gpickle.gz')  # removed in NetworkX 3.x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gpickle.gz:               Wall time: 273 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "print('gpickle.gz:              ', end=' ', flush=True)\n",
    "with open('datasets/git-commit_graph.gpickle.gz', 'wb') as f:\n",
    "    pickle.dump(graph_git, f, pickle.HIGHEST_PROTOCOL)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
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       "          source     target\n",
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       "[79664 rows x 2 columns]"
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     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "graph_git_df = nx.to_pandas_edgelist(graph_git)\n",
    "graph_git_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 1.07 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "graph_git_df.to_pickle('datasets/git-commit_graph.df_edgelist.pickle.gz')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 1.04 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "graph_git_df.to_csv('datasets/git-commit_graph.df_edgelist.csv.gz')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Both `to_feather()` and `to_parquet()` need `pyarrow` module installed (the latter might use `fastparquet` instead)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 587 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "try:\n",
    "    graph_git_df.to_feather('datasets/git-commit_graph.df_edgelist.feather')\n",
    "except ImportError:\n",
    "    print(\"Missing optional dependency 'pyarrow' required to save dataframe to the feather format\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 1.18 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "try:\n",
    "    graph_git_df.to_parquet('datasets/git-commit_graph.df_edgelist.parquet')\n",
    "except ImportError:\n",
    "    print(\"Missing optional dependency 'pyarrow' or 'fastparquet' required to save dataframe to the parquet format\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`to_hdf()` needs `tables` module installed (PyTables)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 2.6 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "try:\n",
    "    graph_git_df.to_hdf('datasets/git-commit_graph.df_edgelist.hdf5', 'df_edgelist', mode='w', complevel=6)\n",
    "except ImportError:\n",
    "    print(\"Missing optional dependency 'table' required to save dataframe to the HDF5 format\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comparing the filesize of different graph output formats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Previously `!dir datasets` was used, but\n",
    "- it is not portable (on Linux it only lists files, instead of showing among others file size information)\n",
    "- on MS Windows where it works for this purpose, it includes unnecessary information"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['git-commit_graph-df_reachability_sample.csv.gz      338527',\n",
       " 'git-commit_graph.adjlist.txt.gz                     581624',\n",
       " 'git-commit_graph.df_edgelist.csv.gz                 808989',\n",
       " 'git-commit_graph.df_edgelist.pickle.gz              668474',\n",
       " 'git-commit_graph.df_nodedata.csv.gz                 773957',\n",
       " 'git-commit_graph.edgelist.txt.gz                    606109',\n",
       " 'git-commit_graph.gexf.gz                           1524987',\n",
       " 'git-commit_graph.gpickle.gz                        3851388',\n",
       " 'git-commit_graph.graphml.gz                        1109122',\n",
       " 'git-commit_graph.info.csv.gz                       1785780',\n",
       " 'git-commit_graph.info.pickle.gz                    1467752',\n",
       " 'git-commit_graph.multiline_adjlist.txt.gz           638575',\n",
       " 'git-commit_graph.pajek.gz                           876408']"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[\"{name:<50} {size:>7}\".format(name=p.name,size=p.stat().st_size) for p in Path(\"datasets\").glob(\"git*.gz\")]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['git-commit_graph.adjlist.txt                       1434939',\n",
       " 'git-commit_graph.df_edgelist.csv                   4383858',\n",
       " 'git-commit_graph.df_edgelist.feather               1918282',\n",
       " 'git-commit_graph.df_edgelist.hdf5                  2421869',\n",
       " 'git-commit_graph.df_edgelist.parquet               1617488',\n",
       " 'git-commit_graph.edgelist.txt                      1832272',\n",
       " 'git-commit_graph.hdf5                              3803473',\n",
       " 'git-commit_graph.info.hdf5                         1382956',\n",
       " 'git-commit_graph.info.parquet                      3164039',\n",
       " 'git-commit_graph.multiline_adjlist.txt             1801780']"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[\"{name:<50} {size:>7}\".format(name=p.name,size=p.stat().st_size) for p in Path(\"datasets\").glob(\"git*\") if not p.match(\"*.gz\")]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ":::{.callout-note}\n",
    "\n",
    "the information below was gathered for `git log --all`, not `git log --branches` as it is done now, so the exact sizes will be different\n",
    "\n",
    ":::"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>git-commit_graph.multiline_adjlist.txt</td>\n",
       "      <td>3610938</td>\n",
       "      <td>3610938</td>\n",
       "      <td>0.456</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>git-commit_graph.edgelist.txt</td>\n",
       "      <td>3692282</td>\n",
       "      <td>3692282</td>\n",
       "      <td>0.624</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>git-commit_graph.gpickle.gz</td>\n",
       "      <td>3254690</td>\n",
       "      <td>7712162</td>\n",
       "      <td>4.920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>git-commit_graph.gexf.gz</td>\n",
       "      <td>3063783</td>\n",
       "      <td>16419236</td>\n",
       "      <td>9.490</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>git-commit_graph.graphml.gz</td>\n",
       "      <td>2231397</td>\n",
       "      <td>10305482</td>\n",
       "      <td>4.740</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>git-commit_graph.pajek.gz</td>\n",
       "      <td>1754236</td>\n",
       "      <td>6682509</td>\n",
       "      <td>6.740</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>git-commit_graph.df_edgelist.pickle.gz</td>\n",
       "      <td>1332691</td>\n",
       "      <td>2736191</td>\n",
       "      <td>1.900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>git-commit_graph.df_edgelist.feather</td>\n",
       "      <td>3857818</td>\n",
       "      <td>3857818</td>\n",
       "      <td>0.487</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>git-commit_graph.df_edgelist.parquet</td>\n",
       "      <td>3116020</td>\n",
       "      <td>3116020</td>\n",
       "      <td>0.333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>git-commit_graph.df_edgelist.csv</td>\n",
       "      <td>4383858</td>\n",
       "      <td>4383858</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>git-commit_graph.df_edgelist.csv.gz</td>\n",
       "      <td>1629263</td>\n",
       "      <td>4383858</td>\n",
       "      <td>1.200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>git-commit_graph.df_edgelist.hdf5</td>\n",
       "      <td>3808521</td>\n",
       "      <td>5077784</td>\n",
       "      <td>0.244</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                  filename  size [bytes]  \\\n",
       "0             git-commit_graph.adjlist.txt       2875179   \n",
       "1          git-commit_graph.adjlist.txt.gz       1173712   \n",
       "2   git-commit_graph.multiline_adjlist.txt       3610938   \n",
       "3            git-commit_graph.edgelist.txt       3692282   \n",
       "4              git-commit_graph.gpickle.gz       3254690   \n",
       "5                 git-commit_graph.gexf.gz       3063783   \n",
       "6              git-commit_graph.graphml.gz       2231397   \n",
       "7                git-commit_graph.pajek.gz       1754236   \n",
       "8   git-commit_graph.df_edgelist.pickle.gz       1332691   \n",
       "9     git-commit_graph.df_edgelist.feather       3857818   \n",
       "10    git-commit_graph.df_edgelist.parquet       3116020   \n",
       "11        git-commit_graph.df_edgelist.csv       4383858   \n",
       "12     git-commit_graph.df_edgelist.csv.gz       1629263   \n",
       "13       git-commit_graph.df_edgelist.hdf5       3808521   \n",
       "\n",
       "    size uncompressed [bytes]  time [s]  \n",
       "0                     2875179       NaN  \n",
       "1                     2875369     0.910  \n",
       "2                     3610938     0.456  \n",
       "3                     3692282     0.624  \n",
       "4                     7712162     4.920  \n",
       "5                    16419236     9.490  \n",
       "6                    10305482     4.740  \n",
       "7                     6682509     6.740  \n",
       "8                     2736191     1.900  \n",
       "9                     3857818     0.487  \n",
       "10                    3116020     0.333  \n",
       "11                    4383858       NaN  \n",
       "12                    4383858     1.200  \n",
       "13                    5077784     0.244  "
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import io\n",
    "\n",
    "csv = u\"\"\"filename;size [bytes];size uncompressed [bytes];time [s]\n",
    "git-commit_graph.adjlist.txt;2875179;2875179\n",
    "git-commit_graph.adjlist.txt.gz;1173712;2875369;0.910\n",
    "git-commit_graph.multiline_adjlist.txt;3610938;3610938;0.456\n",
    "git-commit_graph.edgelist.txt;3692282;3692282;0.624\n",
    "git-commit_graph.gpickle.gz;3254690;7712162;4.92\n",
    "git-commit_graph.gexf.gz;3063783;16419236;9.49\n",
    "git-commit_graph.graphml.gz;2231397;10305482;4.74\n",
    "git-commit_graph.pajek.gz;1754236;6682509;6.74\n",
    "git-commit_graph.df_edgelist.pickle.gz;1332691;2736191;1.9\n",
    "git-commit_graph.df_edgelist.feather;3857818;3857818;0.487\n",
    "git-commit_graph.df_edgelist.parquet;3116020;3116020;0.333\n",
    "git-commit_graph.df_edgelist.csv;4383858;4383858\n",
    "git-commit_graph.df_edgelist.csv.gz;1629263;4383858;1.2\n",
    "git-commit_graph.df_edgelist.hdf5;3808521;5077784;0.244\n",
    "\"\"\"\n",
    "\n",
    "csv_stream = io.StringIO(csv)\n",
    "table_sizes=pd.read_csv(csv_stream,sep=';') # ,index_col=0\n",
    "table_sizes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "filename                      object\n",
       "size [bytes]                   int64\n",
       "size uncompressed [bytes]      int64\n",
       "time [s]                     float64\n",
       "dtype: object"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table_sizes.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>filename</th>\n",
       "      <th>size [bytes]</th>\n",
       "      <th>size uncompressed [bytes]</th>\n",
       "      <th>time [s]</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>git-commit_graph.adjlist.txt.gz</td>\n",
       "      <td>1173712</td>\n",
       "      <td>2875369</td>\n",
       "      <td>0.910</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>git-commit_graph.df_edgelist.pickle.gz</td>\n",
       "      <td>1332691</td>\n",
       "      <td>2736191</td>\n",
       "      <td>1.900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>git-commit_graph.df_edgelist.csv.gz</td>\n",
       "      <td>1629263</td>\n",
       "      <td>4383858</td>\n",
       "      <td>1.200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>git-commit_graph.pajek.gz</td>\n",
       "      <td>1754236</td>\n",
       "      <td>6682509</td>\n",
       "      <td>6.740</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>git-commit_graph.graphml.gz</td>\n",
       "      <td>2231397</td>\n",
       "      <td>10305482</td>\n",
       "      <td>4.740</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>git-commit_graph.adjlist.txt</td>\n",
       "      <td>2875179</td>\n",
       "      <td>2875179</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>git-commit_graph.gexf.gz</td>\n",
       "      <td>3063783</td>\n",
       "      <td>16419236</td>\n",
       "      <td>9.490</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>git-commit_graph.df_edgelist.parquet</td>\n",
       "      <td>3116020</td>\n",
       "      <td>3116020</td>\n",
       "      <td>0.333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>git-commit_graph.gpickle.gz</td>\n",
       "      <td>3254690</td>\n",
       "      <td>7712162</td>\n",
       "      <td>4.920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>git-commit_graph.multiline_adjlist.txt</td>\n",
       "      <td>3610938</td>\n",
       "      <td>3610938</td>\n",
       "      <td>0.456</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>git-commit_graph.edgelist.txt</td>\n",
       "      <td>3692282</td>\n",
       "      <td>3692282</td>\n",
       "      <td>0.624</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>git-commit_graph.df_edgelist.hdf5</td>\n",
       "      <td>3808521</td>\n",
       "      <td>5077784</td>\n",
       "      <td>0.244</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>git-commit_graph.df_edgelist.feather</td>\n",
       "      <td>3857818</td>\n",
       "      <td>3857818</td>\n",
       "      <td>0.487</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>git-commit_graph.df_edgelist.csv</td>\n",
       "      <td>4383858</td>\n",
       "      <td>4383858</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                  filename  size [bytes]  \\\n",
       "1          git-commit_graph.adjlist.txt.gz       1173712   \n",
       "8   git-commit_graph.df_edgelist.pickle.gz       1332691   \n",
       "12     git-commit_graph.df_edgelist.csv.gz       1629263   \n",
       "7                git-commit_graph.pajek.gz       1754236   \n",
       "6              git-commit_graph.graphml.gz       2231397   \n",
       "0             git-commit_graph.adjlist.txt       2875179   \n",
       "5                 git-commit_graph.gexf.gz       3063783   \n",
       "10    git-commit_graph.df_edgelist.parquet       3116020   \n",
       "4              git-commit_graph.gpickle.gz       3254690   \n",
       "2   git-commit_graph.multiline_adjlist.txt       3610938   \n",
       "3            git-commit_graph.edgelist.txt       3692282   \n",
       "13       git-commit_graph.df_edgelist.hdf5       3808521   \n",
       "9     git-commit_graph.df_edgelist.feather       3857818   \n",
       "11        git-commit_graph.df_edgelist.csv       4383858   \n",
       "\n",
       "    size uncompressed [bytes]  time [s]  \n",
       "1                     2875369     0.910  \n",
       "8                     2736191     1.900  \n",
       "12                    4383858     1.200  \n",
       "7                     6682509     6.740  \n",
       "6                    10305482     4.740  \n",
       "0                     2875179       NaN  \n",
       "5                    16419236     9.490  \n",
       "10                    3116020     0.333  \n",
       "4                     7712162     4.920  \n",
       "2                     3610938     0.456  \n",
       "3                     3692282     0.624  \n",
       "13                    5077784     0.244  \n",
       "9                     3857818     0.487  \n",
       "11                    4383858       NaN  "
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table_sizes.sort_values(by='size [bytes]')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>filename</th>\n",
       "      <th>size [bytes]</th>\n",
       "      <th>size uncompressed [bytes]</th>\n",
       "      <th>time [s]</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>git-commit_graph.df_edgelist.pickle.gz</td>\n",
       "      <td>1332691</td>\n",
       "      <td>2736191</td>\n",
       "      <td>1.900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>git-commit_graph.adjlist.txt</td>\n",
       "      <td>2875179</td>\n",
       "      <td>2875179</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>git-commit_graph.adjlist.txt.gz</td>\n",
       "      <td>1173712</td>\n",
       "      <td>2875369</td>\n",
       "      <td>0.910</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>git-commit_graph.df_edgelist.parquet</td>\n",
       "      <td>3116020</td>\n",
       "      <td>3116020</td>\n",
       "      <td>0.333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>git-commit_graph.multiline_adjlist.txt</td>\n",
       "      <td>3610938</td>\n",
       "      <td>3610938</td>\n",
       "      <td>0.456</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>git-commit_graph.edgelist.txt</td>\n",
       "      <td>3692282</td>\n",
       "      <td>3692282</td>\n",
       "      <td>0.624</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>git-commit_graph.df_edgelist.feather</td>\n",
       "      <td>3857818</td>\n",
       "      <td>3857818</td>\n",
       "      <td>0.487</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>git-commit_graph.df_edgelist.csv</td>\n",
       "      <td>4383858</td>\n",
       "      <td>4383858</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>git-commit_graph.df_edgelist.csv.gz</td>\n",
       "      <td>1629263</td>\n",
       "      <td>4383858</td>\n",
       "      <td>1.200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>git-commit_graph.df_edgelist.hdf5</td>\n",
       "      <td>3808521</td>\n",
       "      <td>5077784</td>\n",
       "      <td>0.244</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>git-commit_graph.pajek.gz</td>\n",
       "      <td>1754236</td>\n",
       "      <td>6682509</td>\n",
       "      <td>6.740</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>git-commit_graph.gpickle.gz</td>\n",
       "      <td>3254690</td>\n",
       "      <td>7712162</td>\n",
       "      <td>4.920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>git-commit_graph.graphml.gz</td>\n",
       "      <td>2231397</td>\n",
       "      <td>10305482</td>\n",
       "      <td>4.740</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>git-commit_graph.gexf.gz</td>\n",
       "      <td>3063783</td>\n",
       "      <td>16419236</td>\n",
       "      <td>9.490</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                  filename  size [bytes]  \\\n",
       "8   git-commit_graph.df_edgelist.pickle.gz       1332691   \n",
       "0             git-commit_graph.adjlist.txt       2875179   \n",
       "1          git-commit_graph.adjlist.txt.gz       1173712   \n",
       "10    git-commit_graph.df_edgelist.parquet       3116020   \n",
       "2   git-commit_graph.multiline_adjlist.txt       3610938   \n",
       "3            git-commit_graph.edgelist.txt       3692282   \n",
       "9     git-commit_graph.df_edgelist.feather       3857818   \n",
       "11        git-commit_graph.df_edgelist.csv       4383858   \n",
       "12     git-commit_graph.df_edgelist.csv.gz       1629263   \n",
       "13       git-commit_graph.df_edgelist.hdf5       3808521   \n",
       "7                git-commit_graph.pajek.gz       1754236   \n",
       "4              git-commit_graph.gpickle.gz       3254690   \n",
       "6              git-commit_graph.graphml.gz       2231397   \n",
       "5                 git-commit_graph.gexf.gz       3063783   \n",
       "\n",
       "    size uncompressed [bytes]  time [s]  \n",
       "8                     2736191     1.900  \n",
       "0                     2875179       NaN  \n",
       "1                     2875369     0.910  \n",
       "10                    3116020     0.333  \n",
       "2                     3610938     0.456  \n",
       "3                     3692282     0.624  \n",
       "9                     3857818     0.487  \n",
       "11                    4383858       NaN  \n",
       "12                    4383858     1.200  \n",
       "13                    5077784     0.244  \n",
       "7                     6682509     6.740  \n",
       "4                     7712162     4.920  \n",
       "6                    10305482     4.740  \n",
       "5                    16419236     9.490  "
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table_sizes.sort_values(by='size uncompressed [bytes]')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Summary of findings"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<u>Storing DataFrame of edgelist data</u>\n",
    "\n",
    "The DataFrame is created using `nx.to_pandas_edgelist(graph)`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The smallest file is the result of storing DataFrame of edgelist data as gzipped pickle (written using Pandas' `to_pickle()`) - the **\\*.df_edgelist.pickle.gz** file.\n",
    "\n",
    "- Advantages:\n",
    "  - 2nd smallest size\n",
    "  - no extra modules to install\n",
    "  - preserves types\n",
    "- Disadvantages:\n",
    "  - Python-specific\n",
    "  - unsafe\n",
    "  - slow (?)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next smallest is, surprisingly, gzipped CSV representing DataFrame of edgelist data (written using Pandas' `to_csv()`) - the **\\*.df_edgelist.csv.gz** file.\n",
    "\n",
    "- Advantages:\n",
    "  - 3rd smallest size\n",
    "  - no extra modules to install\n",
    "  - universal format\n",
    "- Disadvantages:\n",
    "  - slow (?)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The fast interchange formats, [Feather](https://github.com/wesm/feather) and [Parquet](https://parquet.apache.org/) turned out to produce quite large files; they are however 4th smallest and 2nd smallest, respectively, among uncompressed formats.\n",
    "\n",
    "**_Feather_** provides a binary columnar serialization for data frames. It is designed to make reading and writing data frames efficient, and to make sharing data across data analysis languages easy.\n",
    "\n",
    "Feather is designed to faithfully serialize and de-serialize `DataFrame`s, supporting all of the pandas dtypes, including extension dtypes such as categorical and datetime with tz.\n",
    "\n",
    "**_Apache Parquet_** provides a _partitioned_ binary columnar serialization for data frames. It is designed to make reading and writing data frames efficient, and to make sharing data across data analysis languages easy. Parquet can use a variety of compression techniques (default is to use 'snappy') to shrink the file size as much as possible while still maintaining good read performance.\n",
    "\n",
    "Parquet is designed to faithfully serialize and de-serialize `DataFrame`s, supporting all of the pandas dtypes, including extension dtypes such as datetime with tz.\n",
    "\n",
    "- Advantages:\n",
    "  - universal, cross language\n",
    "  - preserves types\n",
    "  - fast\n",
    "  - [support for CUDA](https://arrow.apache.org/docs/python/cuda.html)\n",
    "- Disadvantages:\n",
    "  - requires `pyarrow` package to be installed\n",
    "  - quite large file size"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The **_HDF5_** format has the advantage of being able to store multiple `DataFrame`s in a single file, for example one `DataFrame` to hold edgelist data to define the graph connections, and one `DataFrame` holding various per vertex (per node) rechablity index data.  Unfortunately, even internally compressed it has one of larger file sizes (and largest compressed).\n",
    "\n",
    "[Hierarchical Data Format (HDF)](https://portal.hdfgroup.org/display/HDF5/HDF5) is self-describing, allowing an application to interpret the structure and contents of a file with no outside information. One HDF file can hold a mix of related objects which can be accessed as a group or as individual objects.\n",
    "\n",
    "The `to_hdf()` method in Pandas uses the `HDFStore` in the background, which in turn utilizes the [PyTables](https://www.pytables.org/) library.\n",
    "\n",
    "- Advantages:\n",
    "  - universal, cross language\n",
    "  - preserves types\n",
    "  - can store multiple `DataFrame`s\n",
    "- Disadvantages:\n",
    "  - large file size\n",
    "  - requires `tables` package to be installed (PyTables)\n",
    "  - slow (?)\n",
    "  - unsafe (because of serializing object-dtype data with pickle)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "<u>Storing NetworkX DiGraph directly</u>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Except for the adjacency lists format (**\\*.adjlist.txt**), which cannot store any additional data (not even per-edge), the multi-line adjacency lists (**\\*.multiline_adjlist.txt**) and edge lists (**\\*.edgelist.txt**) formats have file sizes larger than the Parquet storing `DataFrame` of edge lists.  Note however that they are uncompressed.\n",
    "\n",
    "The adjacency list format can be created directly by appropriate Git command.\n",
    "\n",
    "Because those formats cannot store per-node data, they are not considered for use."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Among specialized graph file formats, which I assume can store both per-node and per-edge data, **_Pajek_** format is smallest (compressed), and 4th smallest among all considered storage formats.  It is also smallest uncompressed among similar file formats."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Writing NetworkX graphs as Python pickles using `write_gpickle()` (\\***.gpickle.gz**) results in quite large file compressed, one of the largest files uncompressed.\n",
    "\n",
    "On the other hand NetworkX graphs can contain any hashable Python object as node (not just integers and strings). For arbitrary data types it may be difficult to represent the data as text. In that case using Python pickles to store the graph data can be used."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Examining computing and storing reachability labels and other per-node data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from git_commit_graph_ext.labelling.levels import *\n",
    "from git_commit_graph_ext.labelling.dfs_intervals import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Computing reachability labels for git.git commit graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "git.git commit graph\n",
      "graph has 63829 nodes and 79664 edges\n",
      "\n",
      "find levels:\n",
      "Wall time: 669 ms\n",
      "\n",
      "find min-post intervals:\n",
      "Wall time: 1.93 s\n",
      "\n",
      "find min-post intervals (graph+tree):\n",
      "Wall time: 1.68 s\n"
     ]
    }
   ],
   "source": [
    "print('git.git commit graph')\n",
    "graph = graph_git\n",
    "\n",
    "print('graph has {} nodes and {} edges'.format(graph.number_of_nodes(), graph.number_of_edges()))\n",
    "\n",
    "print('\\nfind levels:')\n",
    "%time graph.lvl = find_levels(graph)\n",
    "print('\\nfind min-post intervals:')\n",
    "%time graph.mpi = find_dfs_intervals(graph)\n",
    "print('\\nfind min-post intervals (graph+tree):')\n",
    "%time graph.mpi_ext = find_dfs_intervals_extra(graph)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All times to calculate different graph indices for git.git commit graph take around few second."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "git.git commit graph\n"
     ]
    },
    {
     "data": {
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       "<p>63829 rows × 7 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           level  in degree  out degree  degree  f_min    min   post\n",
       "e83c51633      0          1           0       1      1      1      1\n",
       "8bc9a0c76      1          1           1       2      1      1      2\n",
       "e497ea2a9      2          1           1       2      1      1      3\n",
       "bf0c6e839      3          1           1       2      1      1      4\n",
       "19b2860cb      4          1           1       2      1      1      5\n",
       "...          ...        ...         ...     ...    ...    ...    ...\n",
       "e6d102643  21094          1           2       3      1  63662  63825\n",
       "4c6c5054a  21095          1           2       3      1  63662  63826\n",
       "f29945cb3  21096          1           2       3      1  63662  63827\n",
       "b16af9417  21097          1           2       3      1  63662  63828\n",
       "45daf8777  21098          0           2       2      1  63662  63829\n",
       "\n",
       "[63829 rows x 7 columns]"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# calculating parameters of the git.git commit graphs: distribution of in-degree, out-degree and level\n",
    "print('git.git commit graph')\n",
    "graph = graph_git\n",
    "\n",
    "graph_info_df=pd.DataFrame.from_dict(graph.lvl,orient='index').rename(columns={0: 'level'})\n",
    "graph_info_df.index.name='node'\n",
    "graph_info_df['in degree']=pd.Series(dict(graph.in_degree()))\n",
    "graph_info_df['out degree']=pd.Series(dict(graph.out_degree()))\n",
    "graph_info_df['degree']=graph_info_df['in degree']+graph_info_df['out degree']\n",
    "\n",
    "graph_info_df = pd.concat([graph_info_df,\n",
    "                           pd.DataFrame.from_dict(graph.mpi_ext,orient='index',columns=['f_min','min','post'])],\n",
    "                          axis=1,join='inner')\n",
    "\n",
    "graph_info_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "level         int64\n",
       "in degree     int64\n",
       "out degree    int64\n",
       "degree        int64\n",
       "f_min         int64\n",
       "min           int64\n",
       "post          int64\n",
       "dtype: object"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "graph_info_df.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['level', 'in degree', 'out degree', 'degree', 'f_min', 'min', 'post'], dtype='object')"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "graph_info_df.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>level</th>\n",
       "      <th>in degree</th>\n",
       "      <th>out degree</th>\n",
       "      <th>degree</th>\n",
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       "      <th>count</th>\n",
       "      <td>63829.000000</td>\n",
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       "      <td>63829.000000</td>\n",
       "      <td>63829.000000</td>\n",
       "      <td>63829.000000</td>\n",
       "      <td>63829.000000</td>\n",
       "      <td>63829.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>11774.655439</td>\n",
       "      <td>1.248085</td>\n",
       "      <td>1.248085</td>\n",
       "      <td>2.496169</td>\n",
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>6198.793361</td>\n",
       "      <td>1.556817</td>\n",
       "      <td>0.436128</td>\n",
       "      <td>1.602244</td>\n",
       "      <td>10631.734068</td>\n",
       "      <td>21750.776061</td>\n",
       "      <td>18425.989503</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>7003.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>15958.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
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       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>21878.000000</td>\n",
       "      <td>31915.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>17120.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>43554.000000</td>\n",
       "      <td>47872.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>21136.000000</td>\n",
       "      <td>110.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>111.000000</td>\n",
       "      <td>62308.000000</td>\n",
       "      <td>63662.000000</td>\n",
       "      <td>63829.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              level     in degree    out degree        degree         f_min  \\\n",
       "count  63829.000000  63829.000000  63829.000000  63829.000000  63829.000000   \n",
       "mean   11774.655439      1.248085      1.248085      2.496169   2122.979116   \n",
       "std     6198.793361      1.556817      0.436128      1.602244  10631.734068   \n",
       "min        0.000000      0.000000      0.000000      1.000000      1.000000   \n",
       "25%     7003.000000      1.000000      1.000000      2.000000      1.000000   \n",
       "50%    12695.000000      1.000000      1.000000      2.000000      1.000000   \n",
       "75%    17120.000000      1.000000      1.000000      3.000000      1.000000   \n",
       "max    21136.000000    110.000000     10.000000    111.000000  62308.000000   \n",
       "\n",
       "                min          post  \n",
       "count  63829.000000  63829.000000  \n",
       "mean   23913.162168  31915.000000  \n",
       "std    21750.776061  18425.989503  \n",
       "min        1.000000      1.000000  \n",
       "25%        1.000000  15958.000000  \n",
       "50%    21878.000000  31915.000000  \n",
       "75%    43554.000000  47872.000000  \n",
       "max    63662.000000  63829.000000  "
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "graph_info_df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The git.git repository (state for December 2020) has, in all its branches\n",
    "- around 64k commits\n",
    "- maximum level of around 21k (around 1/3 of number of commits)\n",
    "- mean out-degree of 1.25"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualizing topological level stats for git.git commit graph"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Imports for plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "sns.set()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Histogram for backward topological levels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title('Histogram of levels')\n",
    "plt.xlabel('Level')\n",
    "graph_info_df['level'].plot.hist(bins=50)\n",
    "plt.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot of counts for backward topological levels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "level_counts=graph_info_df['level'].value_counts()\n",
    "\n",
    "level_counts_df=pd.DataFrame({'level counts': level_counts})\n",
    "level_counts_df.index.name='level'\n",
    "level_counts_df.sort_index(inplace=True)\n",
    "level_counts_df.plot()\n",
    "\n",
    "plt.title('%s commit graph - number of nodes with given level' %\n",
    "          'git.git')\n",
    "plt.xlabel('level of node / vertex')\n",
    "plt.ylabel('number of nodes / vertices')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Histogram of counts for backward topological levels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    21137.000000\n",
       "mean         3.019776\n",
       "std          3.477064\n",
       "min          1.000000\n",
       "25%          1.000000\n",
       "50%          2.000000\n",
       "75%          4.000000\n",
       "max        112.000000\n",
       "Name: level, dtype: float64"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "level_counts=graph_info_df['level'].value_counts()\n",
    "\n",
    "plt.title('Histogram of level counts\\n'+'Number of levels with given count of nodes')\n",
    "plt.xlabel('Level value count\\n'+'number of commits with given level')\n",
    "level_counts.plot.hist(bins=50)\n",
    "\n",
    "level_counts.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sanity checking the computed level counts; nodes with backward topological level of zero are sink nodes, with out-degree of 0.\n",
    "\n",
    "Thus the number of nodes with level of 0 should be equal to number of nodes with out-degree of 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "git.git commit graph\n",
      "there are   3 nodes with  in-degree of 0\n",
      "there are   9 nodes with out-degree of 0: ['7d77f2e9c', '1bd90415d', '0ca71b373', '16d6b8ab6', 'cb07fc2a2', '161332a52', '2744b2344', '1db95b00a', 'e83c51633']\n",
      "there are   9 nodes with level of 0\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
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       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>level</th>\n",
       "      <th>in degree</th>\n",
       "      <th>out degree</th>\n",
       "      <th>degree</th>\n",
       "      <th>f_min</th>\n",
       "      <th>min</th>\n",
       "      <th>post</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>e83c51633</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1db95b00a</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>799</td>\n",
       "      <td>799</td>\n",
       "      <td>799</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2744b2344</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1149</td>\n",
       "      <td>1149</td>\n",
       "      <td>1149</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>161332a52</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>5044</td>\n",
       "      <td>5044</td>\n",
       "      <td>5044</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cb07fc2a2</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>8137</td>\n",
       "      <td>8137</td>\n",
       "      <td>8137</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16d6b8ab6</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>10300</td>\n",
       "      <td>10300</td>\n",
       "      <td>10300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0ca71b373</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>28384</td>\n",
       "      <td>28384</td>\n",
       "      <td>28384</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1bd90415d</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>61749</td>\n",
       "      <td>61749</td>\n",
       "      <td>61749</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7d77f2e9c</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>62308</td>\n",
       "      <td>62308</td>\n",
       "      <td>62308</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           level  in degree  out degree  degree  f_min    min   post\n",
       "e83c51633      0          1           0       1      1      1      1\n",
       "1db95b00a      0          1           0       1    799    799    799\n",
       "2744b2344      0          1           0       1   1149   1149   1149\n",
       "161332a52      0          1           0       1   5044   5044   5044\n",
       "cb07fc2a2      0          1           0       1   8137   8137   8137\n",
       "16d6b8ab6      0          1           0       1  10300  10300  10300\n",
       "0ca71b373      0          1           0       1  28384  28384  28384\n",
       "1bd90415d      0          1           0       1  61749  61749  61749\n",
       "7d77f2e9c      0          1           0       1  62308  62308  62308"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# sanity checking level counts\n",
    "\n",
    "print('git.git commit graph')\n",
    "graph = graph_git\n",
    "\n",
    "sinks  =[n for n in graph if graph.out_degree(n) == 0]\n",
    "sources=[n for n in graph if graph.in_degree(n)  == 0]\n",
    "print('there are {:3d} nodes with  in-degree of 0'.format(len(sources)))\n",
    "print('there are {:3d} nodes with out-degree of 0: {}'.format(len(sinks),sinks))\n",
    "print('there are {:3d} nodes with level of 0'.format(level_counts.at[0]))\n",
    "\n",
    "graph_info_df[graph_info_df['level']==0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualizing in-degree and out-degree in git.git commit graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "graph_info_df[['in degree','out degree']].hist(bins=10)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "graph_info_df.hist(column=['in degree','out degree'],bins=10,range=(0,10))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "graph_info_df[['in degree','out degree']].plot.hist(bins=51,alpha=0.4,range=(0,50))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For a graph that follows the power law (for example small-world or scale-free graphs),\n",
    "the distribution of degrees should be a straight line on log-log scale.\n",
    "\n",
    "For example the plot below (taken from the KONECT handbook, Figure 7a)\n",
    "shows the degree distribution and cumulative degree distribution\n",
    "for the Wikipedia election network ([EL](http://konect.cc/networks/elec/)).\n",
    "\n",
    "![The degree distribution and cumulative degree distribution for the Wikipedia election network (EL)](images/konect/KONECT_handbook-fig_7a-degree_distribution_Wikipedia_election_network.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below there is the same graph for the commit graph of the git.git repository"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "degree_count_df=graph_info_df['degree'].value_counts(sort=False)\\\n",
    "                    .to_frame(name='Frequency').rename_axis('degree')\\\n",
    "                    .sort_index()\n",
    "degree_count_df['Degree (d)'] = degree_count_df.index\n",
    "\n",
    "degree_count_df.plot(kind='scatter',x='Degree (d)',y='Frequency',color='#0000ff',\n",
    "                     figsize=(8,7),logx=True,logy=True,\n",
    "                     title='git.git commit graph')\n",
    "sns.set_style('ticks', {\"xtick.major.size\": 20, \"ytick.major.size\": 20})\n",
    "plt.xlim([.8, 1e4])\n",
    "plt.ylim([1., 7e4])\n",
    "plt.show()\n",
    "#degree_count_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that degrees span the range up to around $10^2$ in the case of git.git commit graph, not $10^4$ of the Wikipedia elections network.\n",
    "Note also that degree of 1 is an outlier; it does not lie on the line through other points."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below there is in/outdegree comparison plot for the git.git commit graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>level</th>\n",
       "      <th>in degree</th>\n",
       "      <th>out degree</th>\n",
       "      <th>degree</th>\n",
       "      <th>f_min</th>\n",
       "      <th>min</th>\n",
       "      <th>post</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>e83c51633</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8bc9a0c76</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>e497ea2a9</th>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bf0c6e839</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19b2860cb</th>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>e6d102643</th>\n",
       "      <td>21094</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>63662</td>\n",
       "      <td>63825</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4c6c5054a</th>\n",
       "      <td>21095</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>63662</td>\n",
       "      <td>63826</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>f29945cb3</th>\n",
       "      <td>21096</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>63662</td>\n",
       "      <td>63827</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b16af9417</th>\n",
       "      <td>21097</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>63662</td>\n",
       "      <td>63828</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45daf8777</th>\n",
       "      <td>21098</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>63662</td>\n",
       "      <td>63829</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>63829 rows × 7 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           level  in degree  out degree  degree  f_min    min   post\n",
       "e83c51633      0          1           0       1      1      1      1\n",
       "8bc9a0c76      1          1           1       2      1      1      2\n",
       "e497ea2a9      2          1           1       2      1      1      3\n",
       "bf0c6e839      3          1           1       2      1      1      4\n",
       "19b2860cb      4          1           1       2      1      1      5\n",
       "...          ...        ...         ...     ...    ...    ...    ...\n",
       "e6d102643  21094          1           2       3      1  63662  63825\n",
       "4c6c5054a  21095          1           2       3      1  63662  63826\n",
       "f29945cb3  21096          1           2       3      1  63662  63827\n",
       "b16af9417  21097          1           2       3      1  63662  63828\n",
       "45daf8777  21098          0           2       2      1  63662  63829\n",
       "\n",
       "[63829 rows x 7 columns]"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "graph_info_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "grid=sns.relplot(data=graph_info_df,x='out degree',y='in degree',\n",
    "                 kind='scatter',color='#0000ff')\n",
    "ax=grid.axes[0][0]\n",
    "ax.set_title('git.git commit graph')\n",
    "#ax.set_xscale('log')\n",
    "#ax.set_yscale('log')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualizing min-post intervals in git.git commit graphs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "graph_info_df.hist(column=['f_min','min'],bins=20)\n",
    "graph_info_df[['f_min','min']].plot.hist(bins=50,alpha=0.5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Normalized intervals (interval divide by post-visit order number)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>level</th>\n",
       "      <th>in degree</th>\n",
       "      <th>out degree</th>\n",
       "      <th>degree</th>\n",
       "      <th>f_min</th>\n",
       "      <th>min</th>\n",
       "      <th>post</th>\n",
       "      <th>|interval|</th>\n",
       "      <th>|interval|/post</th>\n",
       "      <th>|f_interval|</th>\n",
       "      <th>|f_interval|/post</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>e83c51633</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8bc9a0c76</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>0.500000</td>\n",
       "      <td>1</td>\n",
       "      <td>0.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>e497ea2a9</th>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>0.666667</td>\n",
       "      <td>2</td>\n",
       "      <td>0.666667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bf0c6e839</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>0.750000</td>\n",
       "      <td>3</td>\n",
       "      <td>0.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19b2860cb</th>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>4</td>\n",
       "      <td>0.800000</td>\n",
       "      <td>4</td>\n",
       "      <td>0.800000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>e6d102643</th>\n",
       "      <td>21094</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>63662</td>\n",
       "      <td>63825</td>\n",
       "      <td>163</td>\n",
       "      <td>0.002554</td>\n",
       "      <td>63824</td>\n",
       "      <td>0.999984</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4c6c5054a</th>\n",
       "      <td>21095</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>63662</td>\n",
       "      <td>63826</td>\n",
       "      <td>164</td>\n",
       "      <td>0.002569</td>\n",
       "      <td>63825</td>\n",
       "      <td>0.999984</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>f29945cb3</th>\n",
       "      <td>21096</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>63662</td>\n",
       "      <td>63827</td>\n",
       "      <td>165</td>\n",
       "      <td>0.002585</td>\n",
       "      <td>63826</td>\n",
       "      <td>0.999984</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b16af9417</th>\n",
       "      <td>21097</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>63662</td>\n",
       "      <td>63828</td>\n",
       "      <td>166</td>\n",
       "      <td>0.002601</td>\n",
       "      <td>63827</td>\n",
       "      <td>0.999984</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45daf8777</th>\n",
       "      <td>21098</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>63662</td>\n",
       "      <td>63829</td>\n",
       "      <td>167</td>\n",
       "      <td>0.002616</td>\n",
       "      <td>63828</td>\n",
       "      <td>0.999984</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>63829 rows × 11 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           level  in degree  out degree  degree  f_min    min   post  \\\n",
       "e83c51633      0          1           0       1      1      1      1   \n",
       "8bc9a0c76      1          1           1       2      1      1      2   \n",
       "e497ea2a9      2          1           1       2      1      1      3   \n",
       "bf0c6e839      3          1           1       2      1      1      4   \n",
       "19b2860cb      4          1           1       2      1      1      5   \n",
       "...          ...        ...         ...     ...    ...    ...    ...   \n",
       "e6d102643  21094          1           2       3      1  63662  63825   \n",
       "4c6c5054a  21095          1           2       3      1  63662  63826   \n",
       "f29945cb3  21096          1           2       3      1  63662  63827   \n",
       "b16af9417  21097          1           2       3      1  63662  63828   \n",
       "45daf8777  21098          0           2       2      1  63662  63829   \n",
       "\n",
       "           |interval|  |interval|/post  |f_interval|  |f_interval|/post  \n",
       "e83c51633           0         0.000000             0           0.000000  \n",
       "8bc9a0c76           1         0.500000             1           0.500000  \n",
       "e497ea2a9           2         0.666667             2           0.666667  \n",
       "bf0c6e839           3         0.750000             3           0.750000  \n",
       "19b2860cb           4         0.800000             4           0.800000  \n",
       "...               ...              ...           ...                ...  \n",
       "e6d102643         163         0.002554         63824           0.999984  \n",
       "4c6c5054a         164         0.002569         63825           0.999984  \n",
       "f29945cb3         165         0.002585         63826           0.999984  \n",
       "b16af9417         166         0.002601         63827           0.999984  \n",
       "45daf8777         167         0.002616         63828           0.999984  \n",
       "\n",
       "[63829 rows x 11 columns]"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "graph_info_df['|interval|']=graph_info_df['post'] - graph_info_df['min']\n",
    "graph_info_df['|interval|/post']=graph_info_df['|interval|']/graph_info_df['post']\n",
    "graph_info_df['|f_interval|']=graph_info_df['post'] - graph_info_df['f_min']\n",
    "graph_info_df['|f_interval|/post']=graph_info_df['|f_interval|']/graph_info_df['post']\n",
    "graph_info_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>level</th>\n",
       "      <th>in degree</th>\n",
       "      <th>out degree</th>\n",
       "      <th>degree</th>\n",
       "      <th>f_min</th>\n",
       "      <th>min</th>\n",
       "      <th>post</th>\n",
       "      <th>|interval|</th>\n",
       "      <th>|interval|/post</th>\n",
       "      <th>|f_interval|</th>\n",
       "      <th>|f_interval|/post</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>63829.000000</td>\n",
       "      <td>63829.000000</td>\n",
       "      <td>63829.000000</td>\n",
       "      <td>63829.000000</td>\n",
       "      <td>63829.000000</td>\n",
       "      <td>63829.000000</td>\n",
       "      <td>63829.000000</td>\n",
       "      <td>63829.000000</td>\n",
       "      <td>63829.000000</td>\n",
       "      <td>63829.000000</td>\n",
       "      <td>63829.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>11774.655439</td>\n",
       "      <td>1.248085</td>\n",
       "      <td>1.248085</td>\n",
       "      <td>2.496169</td>\n",
       "      <td>2122.979116</td>\n",
       "      <td>23913.162168</td>\n",
       "      <td>31915.000000</td>\n",
       "      <td>8001.837832</td>\n",
       "      <td>0.303827</td>\n",
       "      <td>29792.020884</td>\n",
       "      <td>0.947877</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>6198.793361</td>\n",
       "      <td>1.556817</td>\n",
       "      <td>0.436128</td>\n",
       "      <td>1.602244</td>\n",
       "      <td>10631.734068</td>\n",
       "      <td>21750.776061</td>\n",
       "      <td>18425.989503</td>\n",
       "      <td>15664.880755</td>\n",
       "      <td>0.458586</td>\n",
       "      <td>18603.735072</td>\n",
       "      <td>0.212082</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>7003.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>15958.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000037</td>\n",
       "      <td>13660.000000</td>\n",
       "      <td>0.999923</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>12695.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>21878.000000</td>\n",
       "      <td>31915.000000</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>0.000282</td>\n",
       "      <td>29954.000000</td>\n",
       "      <td>0.999966</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>17120.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>43554.000000</td>\n",
       "      <td>47872.000000</td>\n",
       "      <td>7365.000000</td>\n",
       "      <td>0.999864</td>\n",
       "      <td>45942.000000</td>\n",
       "      <td>0.999978</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>21136.000000</td>\n",
       "      <td>110.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>111.000000</td>\n",
       "      <td>62308.000000</td>\n",
       "      <td>63662.000000</td>\n",
       "      <td>63829.000000</td>\n",
       "      <td>61747.000000</td>\n",
       "      <td>0.999984</td>\n",
       "      <td>63828.000000</td>\n",
       "      <td>0.999984</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              level     in degree    out degree        degree         f_min  \\\n",
       "count  63829.000000  63829.000000  63829.000000  63829.000000  63829.000000   \n",
       "mean   11774.655439      1.248085      1.248085      2.496169   2122.979116   \n",
       "std     6198.793361      1.556817      0.436128      1.602244  10631.734068   \n",
       "min        0.000000      0.000000      0.000000      1.000000      1.000000   \n",
       "25%     7003.000000      1.000000      1.000000      2.000000      1.000000   \n",
       "50%    12695.000000      1.000000      1.000000      2.000000      1.000000   \n",
       "75%    17120.000000      1.000000      1.000000      3.000000      1.000000   \n",
       "max    21136.000000    110.000000     10.000000    111.000000  62308.000000   \n",
       "\n",
       "                min          post    |interval|  |interval|/post  \\\n",
       "count  63829.000000  63829.000000  63829.000000     63829.000000   \n",
       "mean   23913.162168  31915.000000   8001.837832         0.303827   \n",
       "std    21750.776061  18425.989503  15664.880755         0.458586   \n",
       "min        1.000000      1.000000      0.000000         0.000000   \n",
       "25%        1.000000  15958.000000      1.000000         0.000037   \n",
       "50%    21878.000000  31915.000000      7.000000         0.000282   \n",
       "75%    43554.000000  47872.000000   7365.000000         0.999864   \n",
       "max    63662.000000  63829.000000  61747.000000         0.999984   \n",
       "\n",
       "       |f_interval|  |f_interval|/post  \n",
       "count  63829.000000       63829.000000  \n",
       "mean   29792.020884           0.947877  \n",
       "std    18603.735072           0.212082  \n",
       "min        0.000000           0.000000  \n",
       "25%    13660.000000           0.999923  \n",
       "50%    29954.000000           0.999966  \n",
       "75%    45942.000000           0.999978  \n",
       "max    63828.000000           0.999984  "
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "graph_info_df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "graph_info_df.hist(column=['min'],bins=50,color='m')\n",
    "graph_info_df.hist(column=['min'],bins=50,log=True,color='m')\n",
    "graph_info_df.hist(column=['f_min'],bins=50,color='#800080')\n",
    "graph_info_df.hist(column=['f_min'],bins=50,log=True,color='#800080')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "graph_info_df.hist(column=['|interval|'],bins=50,log=True)\n",
    "graph_info_df.hist(column=['|interval|/post'],bins=50,log=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "graph_info_df['|interval|/post'].plot.kde(bw_method=0.05,ind=np.linspace(0,1,200))\n",
    "plt.title('kernel density estimator, bw=0.05, logscale')\n",
    "plt.xlabel('|interval|/post')\n",
    "plt.gca().set_yscale(\"log\", nonpositive='clip')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "graph_info_df.hist(column=['|interval|/post'],bins=40,log=True)\n",
    "graph_info_df['|interval|/post'].plot.kde(ind=np.linspace(0,1,500),color='k')\n",
    "plt.title('histogram of relative size of the min-post tree interval\\n'+'kernel density estimator, logscale')\n",
    "plt.xlabel('|interval|/post')\n",
    "plt.gca().set_yscale(\"log\", nonpositive='clip')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "graph_info_df.hist(column=['|f_interval|'],bins=50,color='g')\n",
    "graph_info_df.hist(column=['|f_interval|/post'],bins=50,color='c')\n",
    "graph_info_df.hist(column=['|f_interval|/post'],bins=50,log=True,color='c')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Storing computed reachability labels and related stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'datasets/git-commit_graph.hdf5'"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from shutil import copyfile\n",
    "copyfile('datasets/git-commit_graph.df_edgelist.hdf5', 'datasets/git-commit_graph.hdf5')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pickle.gz:  Wall time: 3.8 s\n",
      "csv.gz:     Wall time: 2.11 s\n",
      "hdf (full): Wall time: 316 ms\n",
      "hdf (appd): Wall time: 321 ms\n"
     ]
    }
   ],
   "source": [
    "print('pickle.gz: ', end=' ', flush=True)\n",
    "%time graph_info_df.to_pickle('datasets/git-commit_graph.info.pickle.gz')\n",
    "print('csv.gz:    ', end=' ', flush=True)\n",
    "%time graph_info_df.to_csv('datasets/git-commit_graph.info.csv.gz')\n",
    "print('hdf (full):', end=' ', flush=True)\n",
    "%time graph_info_df.to_hdf('datasets/git-commit_graph.info.hdf5', 'df', mode='w', complevel=6)\n",
    "print('hdf (appd):', end=' ', flush=True)\n",
    "%time graph_info_df.to_hdf('datasets/git-commit_graph.hdf5', 'df_info', mode='a', complevel=6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Saving to `pickle.gz` and `csv.gz` file format takes few seconds, saving to HDF file format takes less than 0.5s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# feather does not support non-numerical index, IIRC\n",
    "#%time graph_info_df.to_feather('datasets/git-commit_graph.info.feather')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 468 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "try:\n",
    "    graph_info_df.to_parquet('datasets/git-commit_graph.info.parquet')\n",
    "except ImportError:\n",
    "    print(\"Missing optional dependency 'pyarrow' required\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['git-commit_graph.info.csv.gz                       1785780',\n",
       " 'git-commit_graph.info.hdf5                         1382956',\n",
       " 'git-commit_graph.info.parquet                      3164039',\n",
       " 'git-commit_graph.info.pickle.gz                    1465333']"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[\"{name:<50} {size:>7}\".format(name=p.name,size=p.stat().st_size) for p in Path(\"datasets\").glob(\"*.info.*\")]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['git-commit_graph.hdf5                              3803473']"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[\"{name:<50} {size:>7}\".format(name=p.name,size=p.stat().st_size) for p in Path(\"datasets\").glob(\"git-commit_graph.hdf5\")]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the sizes below are for `git log --all`, not current `git log --branches`, but the relative sizes should be similar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>filename</th>\n",
       "      <th>size [bytes]</th>\n",
       "      <th>time [s]</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>datasets/git-commit_graph.info.pickle.gz</td>\n",
       "      <td>2833650</td>\n",
       "      <td>6.800</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>datasets/git-commit_graph.info.csv.gz</td>\n",
       "      <td>3681511</td>\n",
       "      <td>5.260</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>datasets/git-commit_graph.info.parquet</td>\n",
       "      <td>6079159</td>\n",
       "      <td>0.345</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>datasets/git-commit_graph.info.hdf5</td>\n",
       "      <td>2735986</td>\n",
       "      <td>0.674</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>datasets/git-commit_graph.hdf5</td>\n",
       "      <td>6548777</td>\n",
       "      <td>0.672</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                   filename  size [bytes]  time [s]\n",
       "0  datasets/git-commit_graph.info.pickle.gz       2833650     6.800\n",
       "1     datasets/git-commit_graph.info.csv.gz       3681511     5.260\n",
       "2    datasets/git-commit_graph.info.parquet       6079159     0.345\n",
       "3       datasets/git-commit_graph.info.hdf5       2735986     0.674\n",
       "4            datasets/git-commit_graph.hdf5       6548777     0.672"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "csv = u\"\"\"filename;size [bytes];time [s]\n",
    "datasets/git-commit_graph.info.pickle.gz;2833650;6.8\n",
    "datasets/git-commit_graph.info.csv.gz;3681511;5.26\n",
    "datasets/git-commit_graph.info.parquet;6079159;0.345 \n",
    "datasets/git-commit_graph.info.hdf5;2735986;0.674\n",
    "datasets/git-commit_graph.hdf5;6548777;0.672\n",
    "\"\"\"\n",
    "\n",
    "csv_stream = io.StringIO(csv)\n",
    "table_sizes_2=pd.read_csv(csv_stream,sep=';') # ,index_col=0\n",
    "table_sizes_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>filename</th>\n",
       "      <th>size [bytes]</th>\n",
       "      <th>time [s]</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>datasets/git-commit_graph.info.hdf5</td>\n",
       "      <td>2735986</td>\n",
       "      <td>0.674</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>datasets/git-commit_graph.info.pickle.gz</td>\n",
       "      <td>2833650</td>\n",
       "      <td>6.800</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>datasets/git-commit_graph.info.csv.gz</td>\n",
       "      <td>3681511</td>\n",
       "      <td>5.260</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>datasets/git-commit_graph.info.parquet</td>\n",
       "      <td>6079159</td>\n",
       "      <td>0.345</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>datasets/git-commit_graph.hdf5</td>\n",
       "      <td>6548777</td>\n",
       "      <td>0.672</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                   filename  size [bytes]  time [s]\n",
       "3       datasets/git-commit_graph.info.hdf5       2735986     0.674\n",
       "0  datasets/git-commit_graph.info.pickle.gz       2833650     6.800\n",
       "1     datasets/git-commit_graph.info.csv.gz       3681511     5.260\n",
       "2    datasets/git-commit_graph.info.parquet       6079159     0.345\n",
       "4            datasets/git-commit_graph.hdf5       6548777     0.672"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table_sizes_2.sort_values(by='size [bytes]')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>filename</th>\n",
       "      <th>size [bytes]</th>\n",
       "      <th>time [s]</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>datasets/git-commit_graph.info.parquet</td>\n",
       "      <td>6079159</td>\n",
       "      <td>0.345</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>datasets/git-commit_graph.hdf5</td>\n",
       "      <td>6548777</td>\n",
       "      <td>0.672</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>datasets/git-commit_graph.info.hdf5</td>\n",
       "      <td>2735986</td>\n",
       "      <td>0.674</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>datasets/git-commit_graph.info.csv.gz</td>\n",
       "      <td>3681511</td>\n",
       "      <td>5.260</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>datasets/git-commit_graph.info.pickle.gz</td>\n",
       "      <td>2833650</td>\n",
       "      <td>6.800</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                   filename  size [bytes]  time [s]\n",
       "2    datasets/git-commit_graph.info.parquet       6079159     0.345\n",
       "4            datasets/git-commit_graph.hdf5       6548777     0.672\n",
       "3       datasets/git-commit_graph.info.hdf5       2735986     0.674\n",
       "1     datasets/git-commit_graph.info.csv.gz       3681511     5.260\n",
       "0  datasets/git-commit_graph.info.pickle.gz       2833650     6.800"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table_sizes_2.sort_values(by='time [s]')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Summary of findings"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Strangely,smallest files size this time is given when storing using the **_HDF5_** (with `compresslevel=6`) format, which is also 2nd fastest.\n",
    "\n",
    "Saving `DataFrame` using the **_Parquet_** format is fastest, but this time it gives the largest size of the file (except for `git-commit_graph.hdf5`, which stores both commit graph in edge list format, and per-node information)\n",
    "\n",
    "Saving as **\\*.pickle.gz** or **\\*.csv.gz** is slowest and second slowest, while both being in the middlle with respect to file sizes (the pickle-based format gives smaller file size)."
   ]
  }
 ],
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   "display_name": "python3",
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