demo/Centrality.ipynb

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    "# Gallery of Centrality\n",
    "\n",
    "Here are some centrality algorithms with pygraphblas.  The first few graphs are of the Zachary Karate graph, and the benchmarks at the end benchmark numerious large SNAP graphs with these algorithms."
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   "source": [
    "## Karate Graph"
   ]
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   "execution_count": 7,
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     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from timeit import repeat\n",
    "from pygraphblas import *\n",
    "from pygraphblas.gviz import *\n",
    "from random import sample\n",
    "\n",
    "karate = dict(Matrix.ssget('Newman/karate'))['karate.mtx'].cast(FP32)\n",
    "\n",
    "# get one-based lables\n",
    "labels1 = karate.cast(INT64).positioni1().reduce_vector(INT64.any_monoid)\n",
    "draw_graph(karate, directed=False, show_weight=False, label_vector=labels1, label_width=5, graph_attr=dict(layout='sfdp'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Degree Centrality"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
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   "source": [
    "def DC(A):\n",
    "    v = Vector.dense(A.type, A.nrows, 1.0)\n",
    "    with FP64.PLUS_PAIR:\n",
    "        return (A @ v) / A.nvals\n",
    "\n",
    "dc = DC(karate) * 100\n",
    "draw_graph(karate, directed=False, label_vector=dc, size_vector=dc, size_scale=1, log_scale=True, show_weight=False, label_width=5, graph_attr=dict(layout='sfdp'))"
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PageRank"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
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    "def PR(A, damping, itermax):\n",
    "    n = A.nrows\n",
    "    r = Vector.sparse(FP32, n)\n",
    "    t = Vector.sparse(FP32, n)\n",
    "    d = A.reduce_vector()\n",
    "    d.assign_scalar(damping, accum=FP32.DIV)\n",
    "    r[:] = 1.0 / n\n",
    "    teleport = (1 - damping) / n\n",
    "    tol = 1e-4\n",
    "    rdiff = 1.0\n",
    "    for i in range(itermax):\n",
    "        # swap t and r\n",
    "        temp = t ; t = r ; r = temp\n",
    "        w = t / d\n",
    "        r[:] = teleport\n",
    "        A.mxv(w, out=r, accum=FP32.PLUS, semiring=FP32.PLUS_SECOND,\n",
    "              desc=descriptor.T0)\n",
    "        t -= r\n",
    "        t.apply(FP32.ABS, out=t)\n",
    "        rdiff = t.reduce_float()\n",
    "        if rdiff <= tol:\n",
    "            break\n",
    "    return r\n",
    "\n",
    "pr = PR(karate, 0.85, 100)\n",
    "draw_graph(karate, directed=False, label_vector=pr, size_vector=pr, size_scale=80, log_scale=True, show_weight=False, label_width=5, graph_attr=dict(layout='sfdp'))"
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   "metadata": {},
   "source": [
    "## Triangle Centrality"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
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    "def TC(A):\n",
    "    T = A.mxm(A, mask=A)\n",
    "    y = T.reduce_vector()\n",
    "    k = y.reduce_float()\n",
    "    return (1/k) * (3 * (A @ y) - 2 * T.mxv(y, semiring=FP64.PLUS_SECOND) + y)\n",
    "\n",
    "tc = TC(karate)\n",
    "draw_graph(karate, directed=False, label_vector=tc, size_vector=tc, size_scale=10, log_scale=True, show_weight=False, label_width=5, graph_attr=dict(layout='sfdp'))"
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Betweenness Centrality"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
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     "execution_count": 11,
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   ],
   "source": [
    "def BC(A, sources=None, k=100):\n",
    "    if sources is None:\n",
    "        sources = sample(list(A.rows), min(k, A.nrows))\n",
    "    AT = A.T\n",
    "    n = A.nrows\n",
    "    ns = len(sources)\n",
    "    paths      = Matrix.dense (FP32, ns, n, 0)\n",
    "    frontier   = Matrix.sparse(FP32, ns, n)\n",
    "    S = []\n",
    "\n",
    "    for i, s in enumerate(sources):\n",
    "        paths[   i, sources[i]] = 1\n",
    "        frontier[i, sources[i]] = 1\n",
    "\n",
    "    frontier.mxm(\n",
    "        A,\n",
    "        out=frontier,\n",
    "        mask=paths,\n",
    "        semiring=FP32.PLUS_FIRST,\n",
    "        desc=descriptor.RC)\n",
    "\n",
    "    for depth in range(n):\n",
    "        if frontier.nvals == 0:\n",
    "            break\n",
    "        s = Matrix.sparse(BOOL, ns, n)\n",
    "        frontier.apply(BOOL.ONE, out=s)\n",
    "        S.append(s)\n",
    "        paths.assign_matrix(frontier, accum=FP32.PLUS)\n",
    "        frontier.mxm(A,\n",
    "            out=frontier,\n",
    "            mask=paths,\n",
    "            semiring=FP32.PLUS_FIRST,\n",
    "            desc=descriptor.RC)\n",
    "\n",
    "    bc = Matrix.dense(FP32, ns, n, 1)\n",
    "    W = Matrix.sparse(FP32, ns, n)\n",
    "\n",
    "    for i in range(depth - 1, 0, -1):\n",
    "        bc.emult(paths, FP32.DIV,\n",
    "                 out=W,\n",
    "                 mask=S[i],\n",
    "                 desc=descriptor.R)\n",
    "        W.mxm(AT, out=W,\n",
    "              mask=S[i-1],\n",
    "              semiring=FP32.PLUS_FIRST,\n",
    "              desc=descriptor.R)\n",
    "        W.emult(paths, FP32.TIMES,\n",
    "                out=bc,\n",
    "                accum=FP32.PLUS)\n",
    "\n",
    "    centrality = Vector.dense (FP32, n, -ns)\n",
    "    bc.reduce_vector(accum=FP32.PLUS,\n",
    "                     out=centrality,\n",
    "                     desc=descriptor.T0)\n",
    "    return centrality\n",
    "\n",
    "bc = BC(karate, k=10)\n",
    "draw_graph(karate, directed=False, label_vector=bc, size_vector=bc, size_scale=0.1, log_scale=True, show_weight=False, label_width=5, graph_attr=dict(layout='sfdp'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Benchmarks\n",
    "\n",
    "Several graphs are benchmarked across all centrality algorithms."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import defaultdict\n",
    "from pathlib import Path\n",
    "from random import seed\n",
    "\n",
    "graphs = [\n",
    "    # ('Newman/karate', -1),\n",
    "    ('SNAP/wiki-Vote', -1),\n",
    "    # ('SNAP/com-Amazon', 0),\n",
    "    # ('SNAP/com-Youtube', -1),\n",
    "    # ('SNAP/as-Skitter', -1),\n",
    "    # ('SNAP/com-LiveJournal', -1),\n",
    "    # ('SNAP/com-Orkut', -1),\n",
    "    # ('SNAP/com-Friendster', -1)\n",
    "]\n",
    "\n",
    "algorithms = [(DC, (), 42), \n",
    "              (PR, (0.85, 10), 42),\n",
    "              (BC, (None, 10), 42),\n",
    "              (TC, (), 42),\n",
    "             ]\n",
    "\n",
    "here = Path('.')\n",
    "\n",
    "results = defaultdict(dict)\n",
    "R = 3\n",
    "N = 1\n",
    "for name, offset in graphs:\n",
    "    print(f'Loading {name}')\n",
    "    G = list(Matrix.ssget(name, binary_cache_dir=here))[offset][1]\n",
    "    print(f'{name} has {G.nvals} edges')\n",
    "    for f, args, random_seed in algorithms:\n",
    "        fname = f.__name__\n",
    "        print(f'Running {fname} {args} on {name} {R} times')\n",
    "        seed(random_seed)\n",
    "        result = repeat(f'{fname}(G, *args)', repeat=R, number=N, globals=locals())\n",
    "        avg = sum(result) / len(result)\n",
    "        print(f'{fname} on {name} took ', avg, f'average for {R} runs')\n",
    "        results[name][fname] = avg\n",
    "\n",
    "results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "labels = []\n",
    "\n",
    "width = 0.5  # the width of the bars\n",
    "fig, ax = plt.subplots()\n",
    "plt.rcParams['figure.figsize'] = [50, 25]\n",
    "\n",
    "for name, runs in results.items():\n",
    "    for a, times in runs.items():\n",
    "        label = name + '-' + a\n",
    "        ax.bar(label, times, width, label=label)\n",
    "        labels.append(label)\n",
    "\n",
    "ax.set_ylabel('Time (log)')\n",
    "ax.set_xticks(np.arange(len(labels)))\n",
    "ax.set_xticklabels(labels)\n",
    "ax.legend()\n",
    "\n",
    "fig.tight_layout()\n",
    "\n",
    "plt.yscale('log')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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