class18_markovclust_R.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Class 14 - Markov Clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "suppressPackageStartupMessages(library(sna))\n",
    "library(readr)\n",
    "suppressPackageStartupMessages(library(igraph))\n",
    "suppressPackageStartupMessages(library(expm))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "markov_cluster <- function(graph) {\n",
    "    adj_mat <- as.matrix(igraph::get.adjacency(graph))\n",
    "    N <- nrow(adj_mat)\n",
    "    trans_mat_new <- (adj_mat + diag(N)) %*% solve(diag(igraph::degree(graph)+1))\n",
    "    trans_mat <- matrix(rep(0, N^2), ncol=N)\n",
    "\n",
    "    iter_count <- 0\n",
    "    \n",
    "    while(norm(trans_mat - trans_mat_new, type=\"f\")/\n",
    "          norm(0.5*(trans_mat + trans_mat_new), type=\"f\") > 0.01 &&\n",
    "          iter_count < 20) {\n",
    "        \n",
    "        ## the new transition matrix becomes the old transition matrix\n",
    "        trans_mat <- trans_mat_new\n",
    "        \n",
    "        ## expansion step; preserves left-stochastic property of the matrix\n",
    "        trans_mat_new <- trans_mat_new %*% trans_mat_new\n",
    "        \n",
    "        ## inflation step; need to renormalize to restore left-stochastic property\n",
    "        trans_mat_new <- trans_mat_new^2\n",
    "        trans_mat_new <- trans_mat_new / matrix(rep(apply(trans_mat_new, 2, sum),N),ncol=N,byrow=TRUE)\n",
    "        \n",
    "        iter_count <- iter_count + 1\n",
    "        print(sprintf(\"just completed iteration: %d\", iter_count))\n",
    "    }\n",
    "    \n",
    "    print(sprintf(\"Number of iterations for markov clustering: %d\", iter_count))\n",
    "    \n",
    "    trans_mat_new[trans_mat_new < 1e-10] <- 0\n",
    "    trans_mat_new[trans_mat_new > 1e-10] <- 1\n",
    "    \n",
    "    cluster_signatures <- unique(as.data.frame(t(trans_mat_new)))\n",
    "    cluster_assignments <- apply(trans_mat_new, 2, function(my_col) {\n",
    "        which(apply(cluster_signatures, 1, function(my_row) {\n",
    "            all(my_row == my_col)\n",
    "        }))\n",
    "    })\n",
    "    names(cluster_assignments) <- rownames(adj_mat)\n",
    "    t(cluster_assignments)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IGRAPH a447bfa UN-- 13 26 -- \n",
      "+ attr: name (v/c)\n"
     ]
    }
   ],
   "source": [
    "test_adjmat <- read.dot(\"testr.dot\")\n",
    "test_adjmat <- test_adjmat + t(test_adjmat)\n",
    "test_igraph <- igraph::graph_from_adjacency_matrix(test_adjmat, mode=\"undirected\")\n",
    "summary(test_igraph)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
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o6q1tGhi/ThDmrh+W/fvn3YsGE2bSb0DghoAIs5cODAzJkzF99hePEuOp8fsvHI\nCF+pUtkiqVK4Pjvr98FhJXoDrdxIO847nDhxIjEx0dbtBa5DQANYxuXLl+Pi4haObnj5bkrK\nCV302cLf/73Wx62RiI6mRy36bOHhtz+WedcS0bPfUFJpYGZmppOTk61bDZyGURwAlvHmm28G\nuTW8eBcR0YYjI0N9a9h0JqJx/XONJv6RS1Hsjx8sJKOq7KOPPrJVU6G3QEADWEBTU9OmTZte\nmE18HhGRSmOfUdrvcp0bu7ew2lOrF/Rzb2B/FIto6Uz68ssvTSaTrRoMvQICGsACDh8+LCDN\nuLgrPz4y8bRWL5i7avGlkn5qnfDNn+58bPLJyYMyzcdPH0zVVZUXLlywTXOhl0BAA1hAQUFB\nmC+J/hqzMXFA9peLN1Y3uMx655l5Hzz9xNTj/75/J4/39/UeLxfycqX8/HzbNBd6CQQ0gAUo\nFApXx6u2zBhy6eGJpxnipRQG/t/xYVp920lhbo5UX19vvSZCL4SABrAAT0/P+ua/f2QY3rrd\nk5o14qTVq26LKdh5dtA9a55sUDm0PqWuiby8vKzdUOhVENAAFhAdHZ1XQS3aKz9+umfiVwfH\nrn5kq59U+X8vfH3vmHPn8mSrtk4zH19eR7WNFBMTY5vmQi+BgAawgAkTJojEzgdSrvy4PSkh\nMbRUwDcRkdDO+NGjv/i4NZ7IDDcfv+sshYSExMfH26S10FsgoAEsQCwWP/XUUx/uIJ2BiMjT\npbmhRWLey+Mxg0LKfKVXhkU3qOi/++i5556zSVOhF0FAA1jGypUrdYJ+L20gInrs9pPJBUHH\nMyLZXbWNTufzZf+4/RQRGU20+AvqJ4t76qmnbNha6BUw1RvAYi5cuDB+/Pgp8c1rHqEz2dHr\n94/3d29wd1JdrnObP/r85IFZDSpa/AVlyr3PnDkTGhpq6/YC1yGgASzp4sWLc+bM0TaWLJ1B\n0weTz5W5hFRWS7v+pM/3UUBI/I4dO5DO0BUIaAALU6lUH3/88eeff15VVenlQq6OVN9EdU0U\nGhr63HPPPfnkkyKRyNZthN4BAQ3QIzIyMo4fPy6VSpVKpYeHR3R0dFxc3PVPA2gFt7wC6BE1\nNTWjRo0aOHCgrRsCvRhGcQBYnslkqqur8/b2tnVDoHdDQANYXm1trclk8vT0tHVDoHdDQANY\nXk1Njbu7u1AotHVDoHdDQANYnlwux0JI0H0IaAALMxqNKECDRSCgASystraWYQb3yIQAACAA\nSURBVBgUoKH7ENAAFiaXyz08PAQCjGGF7kJAA1hYTU0NCtBgEQhoAEsyGo319fUoQINFIKAB\nLKmmpoaIUIAGi0BAA1gSW4C2s7OzdUOgL0BAA1gSCtBgQQhoAIsxGAwKhQIFaLAUBDSAxdTU\n1PB4PA8PD1s3BPoIBDSAxaAADZaFgAawmJqaGtQ3wIIQ0ACWodfrFQoFrhCCBSGgASyjpqaG\nz+ejAA0WhIAGsAy5XO7p6cnn428KLAb/mAAsQy6XowANloWABrAAnU6nVCoR0GBZCGgAC6ip\nqbGzs5NKpbZuCPQpCGgAC0ABGnoC/j0BWAAK0NATENAA3aXT6RobGxHQYHEIaIDuksvlKEBD\nT0BAA3SXXC738vLi8Xi2bgj0NQhogO5CARp6CAIaoFu0Wi0K0NBDENAA3SKXy4VCoZubm60b\nAn0QAhqgW1CAhp6DgAboFhSgoecgoAFunkajaWpqQkBDDxHYugEAvU91dXV1dTWfzzcajSKR\nyNXV1dYtgr4JAQ3QVbW1tWvXrv3ll1/y8/PNG8PDw7OyspYuXerk5GTDtkGfxGMYxtZtAOgF\nNm7c+Mwzz/g4NT4wjsb2J38pGUx0uY6OXKKNR8kg8NmwYcPUqVNt3UzoUxDQANe3atWqN157\n5dV76LHJJLj6wo3RxE8t8tuXfPnLg4Jvv/124cKFNmoj9EEIaIDr+PXXXxfcM++bZ2hqwpUt\nc1ctPpsbYj7go0d/uW/sn//7nd7aIjpy5MioUaNs01DocxDQAJ1paWmJiIi4d2jF8jlXtpzN\nDXlny4yhEcXsj2Kh/tlZv9sLDUT03DeUqxp04cIFLAwNFoGLhACd+f77740tFUum/73lv3sn\nfPL4zyE+tdcevHIejXzp4t69e2fOnGm9JkLfhc95gM5s27Zt5lCSiK78mFYccCIzYs32KRuP\njiip8WhzsI8bjY+j7du3W7uV0EehBw3QmZSUlHvv+/vHgxdjGYZ2nE3YcTbBjm96YsqJ5XMP\nSER68wEjomhHcrINGgp9EWrQAB3SarUSiWTnK8yQ8L83Gk38ErnH9qSE736/TdHsMP+2C+sW\n/Wzeu+tP+tc2n6qqKhs0F/oclDgAOiQSiYRCYYv2qo12fFOob80Lcw7+/vbamMDKX04N/jPv\n7xEdLVpydHS0dkOhj0JAA3SIx+MFBgYWVre/11eqXPuPLUR0sSjQvLGgioKDg63TPOjzENAA\nnZk6derBlA73Dgi+7CLRaPV/X8s5dJGmTJlijZbBLQABDdAhjUYzYsSI4xmUVtzhMSaGF+V/\npY+9P5mKa0Xz5s2zTvOgz0NAA7RDp9OlpaXt3bvXy8vrjmnTX/gftalEs5ILgrzdGsf0zyWi\nmkZ67UeaMWNGRkZGQUEBLr9D92EUB8BVDAZDfn5+VlaWSCSKiYkJCQmpr68fPnx4gKRgyfTA\nlzbcP3vYxQfHn/V3b6iod3txw90r5h4YKCuvUtAjn5DYe9iRI0cuX76cnp4ukUgGDRrk6+tr\n6zcEvRgCGuAKo9FYWFiYlZXF5/NjY2NDQkLMN7IqLCy88847lVUlnq53V9YH6Q12s4enejg3\nPzH1uL1Qu+Ukrd5GUQNGb9u2zcvLi4h0Ol1GRkZ+fr6fn19CQgLGdcDNQUADkMlkKi4uzsjI\nMJlMUVFRERERdnZ2bY7JzMxcuXLlwYMHnUSa0THUz4OMJiqrpROZxBO6vvjii8uXLxeJRK1P\nUSgUKSkpCoUiIiIiNjZWIMC8MLgxCGi4pTEMU1JSkpGRodfrIyIioqKi2o1Ro9G4b98+mUzm\n6+u7a9euU6dOVVVV8fl8f3//CRMmTJ8+3cXFpaOXqKioSE5OZhgmPj5eJpP14JuBPgcBDbco\nhmHKy8vT09PVanV4eHhMTIxQKOzo4LS0tJKSkmnTpt1cL9hoNGZnZ2dnZ7u6uiYkJHh4tF3E\nA6BdCGi4FVVXV6empjY1NYWGhsbGxtrb23dycHNz8/79+4cPHx4YGNjJYdfV0tJy6dKl0tLS\noKCggQMHisXi7jwb3AoQ0HBrqa6uvnTpUkNDg0wmi4uL60pKnjhxwmg0jh8/3iINkMvlFy9e\nVKlUMTExkZGRWDkaOoGAhltFbW1tenp6bW1tYGBgXFxcF0dWVFRUnDp1asqUKRa8dTdb+E5N\nTRWJRIMGDfLz87PUM0Mfg4CGvq+uri4rK6uysjIgICA+Pr7rt982mUwHDhzw8/MbNGiQxVtl\nHorn7e2dkJDQyWVGuGUhoKEvUyqVmZmZ5eXlfn5+cXFxbm5uN3R6VlZWbm7u9OnTO7l+2E1N\nTU0pKSlyuTwsLCwuLq7nXgh6IwQ09E1NTU2ZmZmlpaXe3t7x8fHu7u43+gxqtXrfvn0JCQkh\nISHXP7p7KioqUlJSjEZjXFxc6wkycItDQENf09LSkpmZWVRU5OHhER8fz07tuwlnzpxpbm6+\n/fbbrROXJpOpoKDg0qVLzs7OCQkJnp6eVnhR4DgENPQdarU6Ozu7oKBAKpXGxMT4+/vf9FPV\n1tYeOXJk4sSJVh6zrFar09LSSktLAwICBg4c6ODgYM1XB65BQENfoNVqc3Jy8vLynJycYmNj\nuzlgmWGYQ4cOSaXSoUOHWqqFN6S+vj4lJUWpVEZFRUVHR1877xxuEQho6N3Mi89JJJLo6Ojg\n4ODuVyTy8vLS09OnTZtm27kkxcXFaWlpfD4/Li4Oc8RvTQhosD2VSrV///7k5OTLly87OzsH\nBARMmTIlISGh87PM0SwUCtssPtcdOp1u7969/fv3j4iI6P6zdZPBYMjJycnKyvL09ExISLDg\nWGzoFRDQYEuNjY0ffPDBunXreEZVYhj5ulGLlorklFlG8fEDVq1aNX369GvPYhefS09P5/F4\n0dHRYWFhFpyPd+7cubq6uilTpnBnjl9zc/PFixcrKytDQkLi4+M7n5gOfQkCGmwmLy9v1qxZ\nLXU5L91FM4eSSEBElFXut/nEEBOjy62oOZ2VvPTZ59esWWMuwnZlXdDuUCgUhw8fHjdunLe3\ntwWf1iKqq6tTUlI0Gk3//v3Dw8M7+bpQV1e3f//+/Px8hULh4eHRv3//KVOmdH16DnAHAhps\no6KiYujQobFeFf99kpwlRER1TY5v/N/s7HLfdYs2xwVfJqLT2fT4f+n+h5d89tln7OJzly5d\n0ul0ERERkZGRPTGn4/fff3dwcBg5cqTFn9ki2KF4ndyupbCw8LXXXtuyZYubgzHCn9ydqKaR\nssrIQOJFixa9/vrrHPzggU4goME2xo4dq6s+sWUFCQVERGW10ns/fMLLpWnziq/shQbzYefy\naN5q+vg/n4WGhqrV6sjIyKioqB6abldUVJScnDxt2jSOD27r6HYt27dvf+ihh/r7q5bPpZFR\nZPdXhUZnoN9Tac12Uhh8tm3bNmrUKJs1HW4QAhpsYMeOHQvmzz2xigI9iYj0Brvp//5nZb3r\n4bc/9pUq2xz8/q/085/ee/bs6dHyq16v37dvX0RERExMTA+9hGW1uV3Lb7/9Nu/uuS/eRc9M\nJ3PxQ2cQTH976cIJSQsnnNEb6fUf6ZckyfHjx4cMGWLTtkNXceUyCNxSvvnmm3mjrqQzEX1z\neHRGqf8D485em85EtHg6KRXy2traHr04lpGRIRAIIiMje+4lLEsqlU6cOHHIkCElJSU//PDD\ngw8+uGIuLZ1BrUvTq7dNzSy7MltHaEfvL6Q7B6vnzJnT3Nxsm0bDDUJAg7XpdLrff/992uAr\nPzIM78djw4mIx2Pmrloc/tS7E1974csDY03MlaRxkdBtMbR3796ea1JjY2N+fv6gQYN63ZSQ\n4ODgadOmbd++PdZftXTGVbvO5IQWVLWd5r7qISLN5Q8//NB6TYRuQECDtVVUVGg0msi/pmGX\n1UoLq7ycJZrJA7O2vbz+/EfvxgZVvPXzrFVbp5lPifSn/Px8tVqt+4tlS3MXL1709vbuztRw\nG2pqajpw4MALs6/qOze2SL7YN37F3INtDhaL6JkZ9PXXX5tMJqu2Em4KbjMM1tbY2Eh0ZeQG\nEV2udyOiqQkZg8NLiMjNseXjf2w5kRHx1cGxi6cdlTq1sAcXZRXt3r372mfj8Xjma4Z2dnbs\n4OU2G839YqFQyI5O4/F45rsLajSa6urqkJCQtLQ08225+Xy++QCBQGA+q92nbX3Wta/V0w4e\nPOgg0o+6unL+5s+zXr57n1BgvPb4aYn0ysaKlJSUwYMHX7sXOAUBDdbGjvSqUZKbIxGR0cQn\nImeJxnyAUGCckpD547Hh2Zd9R0YVElFtI3l6evr5+Tk6Ojo6Ojo5OUkkEr1ezx5vMpkMhisD\nPwwGA9u5ZhjGfIDRaDQar0SVXq9nDzCZTEajkWEYuVzu4OCgUqlUKlUnZ137Wl3U7kcIXR3r\nrT8MzAd0/hljPuv8+fPhfiRo9WV4158DI/yrYwIr8yvbGVTn7UoezlRQUICA5j4ENFibt7e3\nj4/PhYLqCH8iolCfWiJSNF81ss3fvYGIlKorG8/n0/DJ0SKRSKFQlJSU6PV6Pp/v4uLi4uLi\n6urq7OwslUodHR0777GmpaWdOnWqqqqKz+f7+/tPmDAhPDycvQnWlClTbmLonsFgMBcKrvth\nYI51o9HInnXdjxCGYdiz9Hp969fS6XTsA5PJpNfrCwsLXVv98ioVrjvODvp6ycZOWu7qQAqF\n4kbfL1gfAhqsymQyXb58eciQIdvO7Ll3DBGRr1TpLNGU1V61oD57hTDMV05EuRWUXkqL4uPZ\n1fcHDhzo7e2t0WgaGxuVSmVlZWVWVpbBYODz+U5OTq6uri6t8Hg8hmG2bNny5ptvZmdnh/qS\nv5QMJiqvpSfqaPDgwdOnT1+0aNHNDaw2d3upVXe4JxiNRpVK1dLSolarW1paVCoV+6ClpcVo\nNDo4OBQ0XjnSxPBe+3HOW/ftsuN3VmKubSLMWOkVENBgJVqttrCwMD8/X6/XP/LII/fdd+CP\nNMPEAcTnMYsmn/zP7kmVCle/v4bZFVV7hvrWhPjWMgy9s4WmTJm6dOnSurq6srKy9PR0rVbr\n4eERGBgYExPDLjinVqsbGxvZyK6urs7JyWEjWyAQ/Oc//zl75tiiyfTDIgpotbZzXgV9fejC\nqncv1NXVrVu3rnXa2opOp1OpVM3NzRqNRq1Ws4/VarVGoyEiPp8vEokkEomTk5NUKvX39xeL\nxU5OTkKhcOuWTWodSUT0zaEx4+NyvF2btHoBEekMAiIyGPlavcDOziTgm4ioqJqUKoqNjbXt\nm4WuwEQV6HENDQ35+fklJSVisTgsLCw0NFQkEr3wwgsbvl772+sU7EWNLZLb33h+UEjZF4s3\n8XnM5Tq32/+17IunNo2Ly/1sD63b53j27Nn+/fuzz8YwDJvUZWVl5qQOCgpqM0parVbX1dXN\nmzevuujshmfps733/nKqbcnVy6Xpm2feXvQZTZ55/6ZNm6xzTU+n07GZ2zp/m5ubW1pa2D9G\nkUjk6OgokUjY/BWLxWwoOzg4tNtCjUbj5eX1wQPNc0fQ7PeWnMuTtfu6b9236/EpJ4ho7U76\nLTs6KyurJ98lWAYCGnoKwzCVlZV5eXnV1dWenp4REREBAQHmiDEYDLNnzz53cu+Xi2lEFDWo\nHN7ZMr22ySnYq75B5fDopFOxgWXv/0rfHBZs3rz5rrvuavf5O0/q5cuXb/r2o71vkETkcPsb\nz08emBXoVc/jXfkHv/nE0JFRhasWbsssozvfpWeXrXz66afNhZFuvnej0cjGrjl/2U5xU1MT\nW1a2s7Nrk7+Ojo5isdjR0fFG+/I6ne6JJ544tm/DkXeoWO7TrPl7DeuKetcnP39o8bSj0wan\nB3gofNwaaxppzMv04bqvHn/88W6+R7ACBDRYnl6vLy4uzsnJ0Wg0gYGBUVFR7d5OW6/XP/fc\nc1+s/3z6YFowhkZGkYM9EVFpDR1Opa8Okpq8fvrpp0mTJnX+cu0mtcFgGDRo0NeLdZMH0s8n\nhkYHVA0KKTOfojMIBjz7xndLN4yKLiCi7w7T6t0un376qVgsZmvZUqmULWe7urqaF7tow2Qy\nabXa1vnbSVGidafY0dHRIjVrhmHYRf11Ot1zzz03SlaxbtFVo6GL5Z6jXnrp/YXbFk44Q0R6\nAy34kAzOQ86cOcOFkg5cF/4ngSU1NTXl5+cXFhaKRKLQ0NDw8PBO5mcLhcL//ve/Dz/88Hvv\nvff4+gMajcZZQho96Q0UHBz88FMLly9f7uLict0X5fF4np6enp6egwYNqq6uLi8vz8jI2LBh\nQ2w/3eSBREQLRp83d5xZx9Ij7QWG4ZFF7I8PTaBP9zSq1er58+crFAq2ll1WVtbY2Gg0GgUC\ngYODg0QiYa8lsoMrOipKBAYGso8lEklHRQmLMK/FER0dHRMTEx4ePm7cuKfWN330D3Jq7z4w\nciU9+Tnl13mc3fMz0rm3QA8aLIAdTZyXl1dRUSGVSiMiIm701lMqlSo9Pb2qqkoikQQFBUVH\nR3ezPbGxsXfHZy9pZ7l/IqIlX97v6qB+76Ht5i0v/0By+zu+++47drBE65ES7Pg2Pp/P4/FM\nJhPDMHw+33yxzsPDw83NraNedk9ovZpdYmKiee299PT0OXPmNNYUPD2NZgz5e6mT3AraeZa+\nPkgx8UOXL1/u6uo6YcKEHh12ApaCgIZuYasZubm5arW6k2qG9Tk4OHz9lHrigHZ2qXXC+H++\nufH5b9lZMKwfjtCnv/dbt24d2/O9FtvrZBimpaVFqVSyvWx26IjRaBQKhU5OTmxJpPPCSHcw\nDFNSUpKamioSiRISEq5dD1qj0Xz66afr168vKipylpDUiWqUpNZRXFzc888///DDD5tMpiNH\njtjZ2Y0bNw79aO5DQMNNYqsZRUVFAoEgLCys82qGlWk0GolEsvs1GhzWzt7d5wa8/uOcC2vf\naT1YeNef9PpWr6KiIolEckM3u7o2spVKpclkahPZ7u7u3bwFrUKhSE5OZm/1HRMT03kjMzIy\nCgoK6urqvLy8YmNjQ0NDzbvUavUff/zh5OQ0ZswY7tzWC9qFj1C4MW2qGYmJiUFBQRz5OzeZ\nTGw+KpVKiURS36xu97CdZwfNGJLWZipHXROJxeI9e/YQkVgsZovO7H/Nfep2s5vH47ET0M1r\nLZlMJrVabQ7r4uLipqYmhmFEIpF59iP73y5Gduuaxh133NGV+wn079/fPDCxDYlEMm7cuD/+\n+CMpKWnkyJHWGVwINwcBDV2l1+vLyspycnJUKlW/fv0mTZrk4eFx/dN6kkqlamhoaGxsbGho\nUCqVbA7a29u7ubmFhoamFWWwFwlba1KLD6fG/Lz86zbbU4to2LBhs2bNajMqQ6FQsMVo8/VA\ndmCc+UrgtcPj+Hz+tZHd1NTU+JeCgoIuRnbrmsbYsWN9fHws8ntzcnIaN27ckSNHkpOTzSty\npKWlbdu2LTk5ubq6WiwWBwcHT548edasWRypWd2aENBwfc3NzYWFhQUFBXZ2djKZLCIiQiKR\nXP80S9Pr9eZuqUKhaGhoMM/wlkqlMpmsdSXh3nvv/WH968/PJv7VHcQDKf2lTi1DI4pbb2zR\n0qFUWvfkbDZzpVJpm5dud0RdY2Nj17Pb1dXV1dW19RNeN7J5PF5RUVFTU1NXaho3ytXVdcyY\nMceOHbO3t7e3t1+2bNmePb/FB9OISBooI7WOSgroue0bn31WunLlymXLlvW6lbL7BtSgoUPX\njs2wZjWjdYQpFAqlUqlSqXg8noODg3nBDalU2tG8kqqqqvDw8HfvU91z21XbH/r4sWDvunce\n2NF640c7aPOFgNzc3Jv44Lk2u9udHHjdfnfr99vQ0FBTU8MuiiQUCs39axcXFzc3NwvW+quq\nqj7//PN169YNCGh8616KCbxqr8FE/3eMPthGw0ffsWXLFmdnZ0u9LnQRAhraYTAYSktLc3Nz\nm5ub+/XrFxER4enpef3TuketVpvHICsUitY9SvO0EalU2vWu3Pvvv//uWyt3v0ZR/a5sUTQ7\nDHz2X1tf/mJYRJH5sJNZ9MBHtPHHnxcsWGDxN8Uur2GO7Otmt1gsZsvWTk5OgwYNsre3N/ey\nzTWcNr8TNze3mx6PkZKSMnr06IfHtrx6D/F5dC5Ptmb71NTiAAd73eRBma/N3+vioC6poQfW\nUnTi9F27dqEfbWUIaLgKW80oLCzk8/k9Ws3Q6XTmrjHbZzQYDAKBwNnZ2VIjHxiGue+++w7t\n2fzlYrothojox2PDP9wx5cLad/h/zVvZ9Sc9/y1NmTZ7/fr1fn5+FnlrXXRtdptHgLAHXNvv\ntre3N5lM7InswSqViojEYnGbXnZXIluv18fFxcV55H72BBHR8YzIrw6Oeez2k05i7dbTgzce\nHXH3yORPn/iJiIrlNO1tevOdj5977rke/I3ANRDQcEV1dXVhYWF5ebmbm1tYWFhwcLAFu0vs\n93e2g9zY2FhfX6/RaMz1CrZSYal1MFozGo3Lly//ZN1/Zg2jhyfQ0Aiy4xMR6Qx0Kou+Pkgn\nsuxWrVo1a9as9PT04cOHBwYGXu8pe4RGo0lNTS0tLQ0KCho0aBCPx+u8321eykMkEtnZ2fF4\nPL1er9Vq2VVJqWuR/dVXX7247MmkD8jVkRiG9/r/zX5jwW8igYGIGIY3/e1/Viudk9e+wx78\n7SH6zwEPtmtv3d/NLQ0B3RcwDNPU1NSVWdHXalPNCA0N7f5QAfPQYHPJgv1ubk4N89dz63xl\nTkpKevPNNw8fPiyyM/pKyWiiKgXxBeKZM2e+9dZb7MKb+fn5KSkpQ4YMCQkJsUKTzBiGyc/P\nT09Pd3JySkhIuG4p6bo1Ezs7O5FIxM5KZ1f012q11F5kT5gwYYDzydfuISIyMTydXiAW6c0v\ntPA//5CI9F8uvrLwv85AA/5J32zYMn/+/J75TUA7MIqjF0tLS/v222/37NlTUlJiMBgkEkn/\n/v1nz5795JNPenm1vZ3ztVQqVUFBQWFhIY/HCwkJCQ8P78oA23a1qVcoFIrWk+vCwsIsfnXr\nhowYMWL//v11dXVnz56trKy0s7Pz9/cfNWpU685geHg4n88/f/68Xq+PjIy0TsNqamqSk5PV\nanVcXFx4eHhXvj2IRCKRSHTtOBOGYTQajXlRf/aBWq02Go3sXQs0Go1Op6urqzOZTGyd5PTp\n08tevHI6n8e0TudiuadWL1j7jy1/v66AxvSnQ4cOIaCtCQHdK6lUqqVLl27YsGFklOnRERR1\nNzlLqKZRnVJ4fsPn51evXv3WW289//zzHZ1eW1ubl5fHVjMGDBhwo9UMvV7f3Nxs7iA3NDRo\ntVrzDU18fHyio6N7aK5zd3h4eEyf3sHaHEREFBoaKhAI/vzzT41GM2BAe5PELUetVqelpbE1\njfHjx3f/o4vH47F16mt3tc5udoCgSqXKyckxmUyya26rYjDxDyT3f3XT3MmDMkVX33NW5k0F\nZWVtT4CehIDufWpraydPntxQcXHrizQi6spGjU44QKafNICev5N+PtH02splbP+69ag4o9HI\nzjRpbGz08/Pr4sSHNiN22T4ytfrKHBwczA7y5ch8wu4ICgoSCARnzpwhoh7KaJPJVFBQcOnS\nJWdn54kTJ1phsk+72c0WxOyvudXXxiMjLxQEOdjrfjw2/Fh65B/vfOQk1rK7xELSKDVtT4Ce\nhIDuZfR6/bx584yKi3teJ6kTEVGTWvy/32/75tDotHVvEZEdnx4YRwNkNP+D7wMCAv79739T\nq2oGwzAymWzMmDGdVDPMt4+qr683LwZknkARFhYmlUq7M7SL4/z9/ceMGXPy5Em9Xp+YmGjZ\ni5ZyuTw5OVmj0cTHx3expmEp7ActOw++sbGxrKyMiKoUV/4VmT066dSjk04ZTPwV/5u/+eSQ\nn08MWzT5BLurUkF+/aw60AX65t9YH/bFF1+knj/2+7+v/F0l5YSeyIz4Yv84neGqGkV8MH36\nBP1j1aopU6YIBILy8nJXV9d2qxmtp+e1qVdIpdLAwMCeW5uNs7y9vcePH3/8+HG9Xj9s2DCL\nfDNoXdNgBzh3/zk7wTCMSqUy/z9VKpXNzc0mk0kkErm5ubm4uAwdOlQmk53OLo5pb9yKgG96\n+/6du/4cmFfxdxHkdDY9O3dYjzYb2sAojt7EYDAEBAQ8NaH6yalXbb/r/afP5cnKvn2pzfEL\n/0Mqh5EffvhhREQEe9mw3el5RCQWi93d3a87Pe+WolQqjx075u7uPnLkyDafakVFRbm5uUql\n0t3dPTo6OiAgoJPnMdc0XFxcEhMT3d3dOzn4prU7rrzzu8OsWLFi7+YPD77Vdja82ZiVLz4w\n7uxTdxwjotPZtOBDu/z8fJlM1hPth3ahB92bHDt2rL62+t7RbbcL7IztHU4Pjacnv0zx9PSs\nqanJy8tju1HscDc3NzdXV9eAgABrDnfrXdiF7Y8ePXrixInRo0cLBAK9Xv/ll1+uX78+MzNT\nJCA3R1KoSG+gxMTE55577oEHHri2r11dXZ2SkmLxmkYn33vY67QRERHXHVe+bNmy9evX/3Rc\n9cC4dvY2qcU1jU63D8wiIp2B3vqZHnroIaSzlSGge5OkpKQBMnLtcrFhdCxptZpff/112LBh\nrq6u4eHhrq6ubm5uuJtGFzk7O0+aNOno0aNHjx719/efN29eZWnWE1Ppy4co7K+18jNKaeef\nyU8/vvDzzz/ftm2beTqiuaYREhIyYMCA7vzO20zzafO9RyqV3tx1Wj8/v1WrVq144Z/hfjRA\nJlz02cMjogofGp/k5tii1Qve+L/Z7z64I9xPbjTRi99Tnd7/vffeu+m3ADcHAd2bVFRU+N/I\n92OJiKSO5OXlNWDAAIFAIBQK0VO+UQ4ODhMmTNi0adNdd901IrRp2weUVylb+cPUtOIAN6eW\nyYMyV8w5+Mo89WO30xOfJw0fPvzMmTN+fn5sTUMqlU6ePPlGl+u8dthM3lGzmwAACHxJREFU\nm2k+/v7+3VyCw2zp0qWFhYUL1vznjXtNbo6q//0+6vvfR80amurmpF4x94C/e0Olgpb/j9Iq\nPPbv32nlqfBACOjeRSAQGEzXP6w1g4ny8vKOHDnSZrudnZ2dnZ1QKBQIBK0fmHOcfWDe22ZL\nXx3C0S6j0fjBBx+MiWz6agntT45fs33qzCFpA2Tle87Hf3to9MWiwG0vr/dxM/7yIi1YU8bO\nTiSiwYMHBwcHd+X5W68S1e6wmR6d5vPxxx9HRka+9NJL/i4/PXY7jYgif3dqVlNGKX28i349\nQ/EDh549+1NYWHs3p4Eedgv9mfUBAQEBv9fcwPENKmpsofnz5w8ZMsT4F51OZzKZ2AetH5v3\n6vX6dre0eXI24vl8PrscBDvD+NotbLhfu1coFPaW65AfffSRpqHgkxVkNNn9cGTEntc/cbDX\nEdHyOQdnv7fkQn7wsfTI2wdmiQT01RIa8/LFc+fOvfHGG+xk62uZRzG2u0qUTYbNPP3003ff\nffcnn3yybdu2d3/JYjeKxeLbb799448P33333b3l/1Tfg1Ecvcn58+eHDRuavJZ8rv7SfM+a\nJ85kh107imPbGXpjq3t1dbVFOrzmcDcYDGxkt4n7NoHeZqN5kTazdiO+TaCb++9tIp593P03\ndV16vd7Hx+e1OYr7xtKFgmC1Tjg6Jt+8d+vpwf/8+t4379v9xJTj7JaPd9GO9Ijc3Fz2R3Zw\nRUdX81xa4UgIqtXqqqoqsVjs4+PTB2Ye9XboQfcmgwcPjoiI/PpQ7mtdWA6BYeibQzR//nxL\nlSPs7Oy6ufRom4g3x/e1ga7RaNhv+uYtWq322s7EtfHd0ZbWjwUCAZ/Pt7e370oAHT9+vLlJ\nMWMoEdHgsJI2e90cW4hI5lVn3jJ3BK3Znvfrr796enoqlUp20T42jj09PcPCwlxdXZ2cnDgS\nx9eSSCRWXi4KOoGA7k14PN4777zz0AP3zBlGcdcrb37/B+VUSXa/9ppVmtYl3Yz4djvm5og3\nGAzmB1qt1tzNb93fv7Y9bGSbi+ys1mX348ePh/uRSwetTisO8JUqJ8Rnm7fIvMnDmTIyMubM\nmcPehatvTIIHm0BA9zLz58/fvfuhRz7Z+NMLFHHllqSk0ohNDM/E8Mzr0O85T2/+RF9+/d/O\n51D0LmySEtFN12fbBLoZm+Ot97LrwOn1+tzcXM8O7vSk1gm3nk788ulNwqsXFfJyIXd3955e\nbgluBQjo3uerr766//7mWe9sf2U+RfWTHUuPSi0KYBjeWz/PGhFZODI6fe1O+t8fdqtWrXr0\n0Udt3VhuuYnByKmpqVlJP7e769VNcxdNPtnm/rNEpGwh3AkbLAIB3fuIxeJff/117dq177zz\njphXPHVQ8dv3H3BzpJpG2nGW/vk19QuO/O23dXfccYetW9oXhIaGFlWT3kjCqy9Jbjk1xEms\neXTS6TbHK5pJriQMSgOLwCiOXqy+vv6XX37Zs2dPYWGhUqn09vaOi4ubPXv2nXfeeUuNU+5R\njY2NXl5e/3tGNyH+742nssKOpke9Mm8fj9f2z2fzSXp3p2dVVRXmBEH3IaABruPhhx/OOP3D\nrleIHXlxNjfk97SYlXf/nc7VDS6F1Z4jowr1Bhr3Ki149KX333/fli2GvgIBDXAdxcXFcXFx\nS+9Q/XMmXcgPXvr1vfNvu2AeJtessT96KfLXl75wdVS/uon2XPLOzs6+9pZUADcBX4QBrkMm\nk/3www/3zL+7vsnvpxOLmtTiNduvWu/13jHnnCTqf2+mH0+IDh/einQGS0EPGqBLfvnll0ce\neSQhuGXFXBoaTuYetNFEJzLpg1+prNF9y5YtkyZNsmkzoU9BQAN0VV5e3iuvvLJt2zYvF1Ns\nILk4UH0TpZdSk0awcOHCt956qy+NOgcuQEAD3Jiqqqo9e/YUFBTU1dV5e3tHRkbOmDGjh+6T\nArc4BDQAAEdhiQAAAI5CQAMAcBQCGgCAoxDQAAAchYAGAOAoBDQAAEchoAEAOAoBDQDAUQho\nAACOQkADAHAUAhoAgKMQ0AAAHIWABgDgKAQ0AABHIaABADgKAQ0AwFEIaAAAjkJAAwBwFAIa\nAICjENAAAByFgAYA4CgENAAARyGgAQA4CgENAMBRCGgAAI5CQAMAcBQCGgCAoxDQAAAchYAG\nAOAoBDQAAEchoAEAOAoBDQDAUQhoAACOQkADAHAUAhoAgKMQ0AAAHIWABgDgKAQ0AABHIaAB\nADgKAQ0AwFEIaAAAjkJAAwBwFAIaAICjENAAAByFgAYA4CgENAAARyGgAQA4CgENAMBRCGgA\nAI5CQAMAcBQCGgCAoxDQAAAchYAGAOAoBDQAAEchoAEAOAoBDQDAUQhoAACOQkADAHAUAhoA\ngKMQ0AAAHIWABgDgKAQ0AABHIaABADgKAQ0AwFEIaAAAjkJAAwBwFAIaAICjENAAAByFgAYA\n4CgENAAARyGgAQA4CgENAMBRCGgAAI5CQAMAcBQCGgCAoxDQAAAchYAGAOAoBDQAAEchoAEA\nOAoBDQDAUQhoAACOQkADAHAUAhoAgKMQ0AAAHIWABgDgKAQ0AABHIaABADgKAQ0AwFEIaAAA\njkJAAwBwFAIaAICjENAAAByFgAYA4CgENAAARyGgAQA4CgENAMBRCGgAAI5CQAMAcBQCGgCA\noxDQAAAchYAGAOAoBDQAAEchoAEAOAoBDQDAUQhoAACOQkADAHAUAhoAgKMQ0AAAHIWABgDg\nKAQ0AABHIaABADgKAQ0AwFEIaAAAjkJAAwBwFAIaAICjENAAAByFgAYA4CgENAAARyGgAQA4\nCgENAMBRCGgAAI5CQAMAcBQCGgCAoxDQAAAchYAGAOAoBDQAAEchoAEAOAoBDQDAUQhoAACO\nQkADAHDU/wMkjPck70KC9gAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(test_igraph)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"just completed iteration: 1\"\n",
      "[1] \"just completed iteration: 2\"\n",
      "[1] \"just completed iteration: 3\"\n",
      "[1] \"just completed iteration: 4\"\n",
      "[1] \"just completed iteration: 5\"\n",
      "[1] \"just completed iteration: 6\"\n",
      "[1] \"just completed iteration: 7\"\n",
      "[1] \"just completed iteration: 8\"\n",
      "[1] \"just completed iteration: 9\"\n",
      "[1] \"Number of iterations for markov clustering: 9\"\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>1</th><th scope=col>2</th><th scope=col>6</th><th scope=col>7</th><th scope=col>4</th><th scope=col>3</th><th scope=col>5</th><th scope=col>8</th><th scope=col>9</th><th scope=col>10</th><th scope=col>12</th><th scope=col>13</th><th scope=col>11</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td><td>2</td><td>3</td><td>3</td><td>3</td><td>3</td><td>3</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{lllllllllllll}\n",
       " 1 & 2 & 6 & 7 & 4 & 3 & 5 & 8 & 9 & 10 & 12 & 13 & 11\\\\\n",
       "\\hline\n",
       "\t 1 & 1 & 1 & 1 & 1 & 1 & 1 & 2 & 3 & 3 & 3 & 3 & 3\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "1 | 2 | 6 | 7 | 4 | 3 | 5 | 8 | 9 | 10 | 12 | 13 | 11 | \n",
       "|---|\n",
       "| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 3 | 3 | 3 | 3 | 3 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "     1 2 6 7 4 3 5 8 9 10 12 13 11\n",
       "[1,] 1 1 1 1 1 1 1 2 3 3  3  3  3 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "markov_cluster(test_igraph)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>protein1</th><th scope=col>protein2</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>AAC3 </td><td>PMR1 </td></tr>\n",
       "\t<tr><td>AAP1 </td><td>GUD1 </td></tr>\n",
       "\t<tr><td>AAP1 </td><td>TRS31</td></tr>\n",
       "\t<tr><td>AAP1 </td><td>GCN3 </td></tr>\n",
       "\t<tr><td>AAP1 </td><td>MDY2 </td></tr>\n",
       "\t<tr><td>AAR2 </td><td>SMD1 </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       " protein1 & protein2\\\\\n",
       "\\hline\n",
       "\t AAC3  & PMR1 \\\\\n",
       "\t AAP1  & GUD1 \\\\\n",
       "\t AAP1  & TRS31\\\\\n",
       "\t AAP1  & GCN3 \\\\\n",
       "\t AAP1  & MDY2 \\\\\n",
       "\t AAR2  & SMD1 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "protein1 | protein2 | \n",
       "|---|---|---|---|---|---|\n",
       "| AAC3  | PMR1  | \n",
       "| AAP1  | GUD1  | \n",
       "| AAP1  | TRS31 | \n",
       "| AAP1  | GCN3  | \n",
       "| AAP1  | MDY2  | \n",
       "| AAR2  | SMD1  | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  protein1 protein2\n",
       "1 AAC3     PMR1    \n",
       "2 AAP1     GUD1    \n",
       "3 AAP1     TRS31   \n",
       "4 AAP1     GCN3    \n",
       "5 AAP1     MDY2    \n",
       "6 AAR2     SMD1    "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "edge_list_df <- readr::read_tsv(\"krogan.sif\", \n",
    "                              col_names=c(\"protein1\",\"protein2\"),\n",
    "                              col_types=cols())\n",
    "head(edge_list_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "summary(test_igraph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IGRAPH b7dae93 UN-- 2674 7079 -- \n",
      "+ attr: name (v/c)\n"
     ]
    }
   ],
   "source": [
    "big_graph <- igraph::graph_from_data_frame(edge_list_df, directed=FALSE)\n",
    "summary(big_graph)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"just completed iteration: 1\"\n",
      "[1] \"just completed iteration: 2\"\n",
      "[1] \"just completed iteration: 3\"\n",
      "[1] \"just completed iteration: 4\"\n",
      "[1] \"just completed iteration: 5\"\n",
      "[1] \"just completed iteration: 6\"\n",
      "[1] \"just completed iteration: 7\"\n",
      "[1] \"just completed iteration: 8\"\n",
      "[1] \"just completed iteration: 9\"\n",
      "[1] \"just completed iteration: 10\"\n",
      "[1] \"just completed iteration: 11\"\n",
      "[1] \"Number of iterations for markov clustering: 11\"\n"
     ]
    }
   ],
   "source": [
    "res <- markov_cluster(big_graph)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>AAC3</th><th scope=col>AAP1</th><th scope=col>AAR2</th><th scope=col>ABF1</th><th scope=col>ABF2</th><th scope=col>ACB1</th><th scope=col>ACE2</th><th scope=col>ACF2</th><th scope=col>ACP1</th><th scope=col>ACS2</th><th scope=col>...</th><th scope=col>JSN1</th><th scope=col>RBL2</th><th scope=col>CUE3</th><th scope=col>PLM2</th><th scope=col>STE13</th><th scope=col>ECM3</th><th scope=col>YPK2</th><th scope=col>CUP2</th><th scope=col>MSE1</th><th scope=col>GSP2</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>1  </td><td>2  </td><td>3  </td><td>4  </td><td>5  </td><td>6  </td><td>7  </td><td>8  </td><td>9  </td><td>10 </td><td>...</td><td>395</td><td>395</td><td>810</td><td>812</td><td>275</td><td>762</td><td>652</td><td>59 </td><td>59 </td><td>817</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll}\n",
       " AAC3 & AAP1 & AAR2 & ABF1 & ABF2 & ACB1 & ACE2 & ACF2 & ACP1 & ACS2 & ... & JSN1 & RBL2 & CUE3 & PLM2 & STE13 & ECM3 & YPK2 & CUP2 & MSE1 & GSP2\\\\\n",
       "\\hline\n",
       "\t 1   & 2   & 3   & 4   & 5   & 6   & 7   & 8   & 9   & 10  & ... & 395 & 395 & 810 & 812 & 275 & 762 & 652 & 59  & 59  & 817\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "AAC3 | AAP1 | AAR2 | ABF1 | ABF2 | ACB1 | ACE2 | ACF2 | ACP1 | ACS2 | ... | JSN1 | RBL2 | CUE3 | PLM2 | STE13 | ECM3 | YPK2 | CUP2 | MSE1 | GSP2 | \n",
       "|---|\n",
       "| 1   | 2   | 3   | 4   | 5   | 6   | 7   | 8   | 9   | 10  | ... | 395 | 395 | 810 | 812 | 275 | 762 | 652 | 59  | 59  | 817 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "     AAC3 AAP1 AAR2 ABF1 ABF2 ACB1 ACE2 ACF2 ACP1 ACS2 ... JSN1 RBL2 CUE3 PLM2\n",
       "[1,] 1    2    3    4    5    6    7    8    9    10   ... 395  395  810  812 \n",
       "     STE13 ECM3 YPK2 CUP2 MSE1 GSP2\n",
       "[1,] 275   762  652  59   59   817 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "844"
      ],
      "text/latex": [
       "844"
      ],
      "text/markdown": [
       "844"
      ],
      "text/plain": [
       "[1] 844"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "max(res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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N4dAzeRVXfr72INEKwUo+DsOcEXJU1d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\nEMwcCGYOBDMHgpkDwcyBYOZAMHP+C8UsAU+fow15AAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"Histogram of table(res)\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}