class10_partyhubs_R.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Class Session 10 - Date Hubs and Party Hubs\n",
    "\n",
    "## Comparing the histograms of local clustering coefficients of date hubs and party hubs\n",
    "\n",
    "In this class, we will analyze the protein-protein interaction network for two classes of yeast proteins, \"date hubs\" and \"party hubs\" as defined by Han et al. in their 2004 study of protein-interaction networks and gene expression (Han et al., Nature, v430, p88, 2004). The authors of that study claimed that there is no difference in the local clustering density, between \"date hubs\" and \"party hubs\".  We will put this to the test. We for each of the \"date hub\" and \"party hub\" proteins, we will compute its local clustering coefficient (Ci) in the protein-protein interaction network.  We will then histogram the Ci values for the two sets of hubs, so that we can compare the distributions of local clustering coefficients for \"date hubs\" and \"party hubs\". We will use a statistical test (Kolmogorov-Smirnov) to compare the two distributions of Ci values."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To get started, we load the packages that we will require:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "suppressPackageStartupMessages(library(igraph))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we'll load the file of hub types `shared/han_hub_data.txt` (which is a two-column TSV file in which the first column is the protein name and the second column contains the string `date` or `party` for each row; the first row of the file contains the column headers), using our old friend `read.table`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "hub_data <- read.table(\"shared/han_hub_data.txt\", \n",
    "                       sep=\"\\t\",\n",
    "                       header=TRUE,\n",
    "                       stringsAsFactors=FALSE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's take a peek at the structure of the `hub_data` data frame, using `head` and `dim`.  Here's what it should look like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 6 × 2</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>Protein</th><th scope=col>HubType</th></tr>\n",
       "\t<tr><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>ACT1 </td><td>date </td></tr>\n",
       "\t<tr><td>ADA2 </td><td>date </td></tr>\n",
       "\t<tr><td>AKR1 </td><td>party</td></tr>\n",
       "\t<tr><td>APC1 </td><td>party</td></tr>\n",
       "\t<tr><td>APC11</td><td>date </td></tr>\n",
       "\t<tr><td>APC2 </td><td>party</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 2\n",
       "\\begin{tabular}{r|ll}\n",
       " Protein & HubType\\\\\n",
       " <chr> & <chr>\\\\\n",
       "\\hline\n",
       "\t ACT1  & date \\\\\n",
       "\t ADA2  & date \\\\\n",
       "\t AKR1  & party\\\\\n",
       "\t APC1  & party\\\\\n",
       "\t APC11 & date \\\\\n",
       "\t APC2  & party\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 2\n",
       "\n",
       "| Protein &lt;chr&gt; | HubType &lt;chr&gt; |\n",
       "|---|---|\n",
       "| ACT1  | date  |\n",
       "| ADA2  | date  |\n",
       "| AKR1  | party |\n",
       "| APC1  | party |\n",
       "| APC11 | date  |\n",
       "| APC2  | party |\n",
       "\n"
      ],
      "text/plain": [
       "  Protein HubType\n",
       "1 ACT1    date   \n",
       "2 ADA2    date   \n",
       "3 AKR1    party  \n",
       "4 APC1    party  \n",
       "5 APC11   date   \n",
       "6 APC2    party  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(hub_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>199</li>\n",
       "\t<li>2</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 199\n",
       "\\item 2\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 199\n",
       "2. 2\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 199   2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dim(hub_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, let's load the file of yeat protein-protein interaction network edges `shared/han_network_edges.txt` (which is a two-column file, with first column is the first protein in the interacting pair, and the second column is the second protein in the interacting pair)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "edge_df <- read.table(\"shared/han_network_edges.txt\",\n",
    "                     sep=\"\\t\",\n",
    "                     header=TRUE,\n",
    "                     stringsAsFactors=FALSE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's take a peek at the data frame `edge_df`, using `head` and `dim`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 6 × 2</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>PROTEINA</th><th scope=col>PROTEINB</th></tr>\n",
       "\t<tr><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>AAR2</td><td>PRP8  </td></tr>\n",
       "\t<tr><td>ABP1</td><td>SRV2  </td></tr>\n",
       "\t<tr><td>ABP1</td><td>ACT1  </td></tr>\n",
       "\t<tr><td>ABP1</td><td>RVS167</td></tr>\n",
       "\t<tr><td>ACT1</td><td>IQG1  </td></tr>\n",
       "\t<tr><td>ACT1</td><td>SRV2  </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 2\n",
       "\\begin{tabular}{r|ll}\n",
       " PROTEINA & PROTEINB\\\\\n",
       " <chr> & <chr>\\\\\n",
       "\\hline\n",
       "\t AAR2 & PRP8  \\\\\n",
       "\t ABP1 & SRV2  \\\\\n",
       "\t ABP1 & ACT1  \\\\\n",
       "\t ABP1 & RVS167\\\\\n",
       "\t ACT1 & IQG1  \\\\\n",
       "\t ACT1 & SRV2  \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 2\n",
       "\n",
       "| PROTEINA &lt;chr&gt; | PROTEINB &lt;chr&gt; |\n",
       "|---|---|\n",
       "| AAR2 | PRP8   |\n",
       "| ABP1 | SRV2   |\n",
       "| ABP1 | ACT1   |\n",
       "| ABP1 | RVS167 |\n",
       "| ACT1 | IQG1   |\n",
       "| ACT1 | SRV2   |\n",
       "\n"
      ],
      "text/plain": [
       "  PROTEINA PROTEINB\n",
       "1 AAR2     PRP8    \n",
       "2 ABP1     SRV2    \n",
       "3 ABP1     ACT1    \n",
       "4 ABP1     RVS167  \n",
       "5 ACT1     IQG1    \n",
       "6 ACT1     SRV2    "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(edge_df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>2523</li>\n",
       "\t<li>2</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 2523\n",
       "\\item 2\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 2523\n",
       "2. 2\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 2523    2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dim(edge_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It will be convenient to let `igraph` compute the local clustering coefficients.  So, we'll want to make an undirected igraph `Graph` object from the edgelist data, using our old friend `graph_from_data_frame`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "ppi_graph <- graph_from_data_frame(edge_df, directed=FALSE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As always, we'll use `summary` to sanity check the `Graph` object:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IGRAPH 0fe33ca UN-- 1344 2523 -- \n",
      "+ attr: name (v/c)\n"
     ]
    }
   ],
   "source": [
    "summary(ppi_graph)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we'll need to get the igraph vertex index values of the proteins that are date hubs or party hubs. To do this, we'll first need to make a data frame containing (in the first column, \"Protein\") the names of the proteins in the vertex order of the `Graph` object, and (in the second column \"order\") the integer vertex indexes of the proteins.  We'll do this using the `data.frame` function, the `V` function in `igraph`, and the `:` operator to get a range of integers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "graph_vertices_df = data.frame(Protein=V(ppi_graph)$name, order=1:length(V(ppi_graph)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's check our work, using the `head` and `dim` functions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 6 × 2</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>Protein</th><th scope=col>order</th></tr>\n",
       "\t<tr><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>AAR2</td><td>1</td></tr>\n",
       "\t<tr><td>ABP1</td><td>2</td></tr>\n",
       "\t<tr><td>ACT1</td><td>3</td></tr>\n",
       "\t<tr><td>ADA2</td><td>4</td></tr>\n",
       "\t<tr><td>AFG3</td><td>5</td></tr>\n",
       "\t<tr><td>AFR1</td><td>6</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 2\n",
       "\\begin{tabular}{r|ll}\n",
       " Protein & order\\\\\n",
       " <fct> & <int>\\\\\n",
       "\\hline\n",
       "\t AAR2 & 1\\\\\n",
       "\t ABP1 & 2\\\\\n",
       "\t ACT1 & 3\\\\\n",
       "\t ADA2 & 4\\\\\n",
       "\t AFG3 & 5\\\\\n",
       "\t AFR1 & 6\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 2\n",
       "\n",
       "| Protein &lt;fct&gt; | order &lt;int&gt; |\n",
       "|---|---|\n",
       "| AAR2 | 1 |\n",
       "| ABP1 | 2 |\n",
       "| ACT1 | 3 |\n",
       "| ADA2 | 4 |\n",
       "| AFG3 | 5 |\n",
       "| AFR1 | 6 |\n",
       "\n"
      ],
      "text/plain": [
       "  Protein order\n",
       "1 AAR2    1    \n",
       "2 ABP1    2    \n",
       "3 ACT1    3    \n",
       "4 ADA2    4    \n",
       "5 AFG3    5    \n",
       "6 AFR1    6    "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(graph_vertices_df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>1344</li>\n",
       "\t<li>2</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1344\n",
       "\\item 2\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1344\n",
       "2. 2\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1344    2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dim(graph_vertices_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we'll need to merge the `graph_vertices_df` data frame with the `hub_data` data frame, to connect the hub type information with the igraph vertex index information.  We'll do this using the `merge` function, passing `x=graph_vertices_df`, `y=hub_data`. We'll also need to specify that the columns to be joined are column 1 of `graph_vertices_df` (using the `on.x` argument to `merge`) and column 2  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "graph_vertices_df <- merge(graph_vertices_df, hub_data, on.x=1, on.y=1, all.x=TRUE, sort=FALSE)\n",
    "graph_vertices_df_sorted <- graph_vertices_df[order(graph_vertices_df$order),c(1,3)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 6 × 2</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>Protein</th><th scope=col>HubType</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;chr&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>200</th><td>AAR2</td><td>NA  </td></tr>\n",
       "\t<tr><th scope=row>201</th><td>ABP1</td><td>NA  </td></tr>\n",
       "\t<tr><th scope=row>1</th><td>ACT1</td><td>date</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>ADA2</td><td>date</td></tr>\n",
       "\t<tr><th scope=row>204</th><td>AFG3</td><td>NA  </td></tr>\n",
       "\t<tr><th scope=row>205</th><td>AFR1</td><td>NA  </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 2\n",
       "\\begin{tabular}{r|ll}\n",
       "  & Protein & HubType\\\\\n",
       "  & <fct> & <chr>\\\\\n",
       "\\hline\n",
       "\t200 & AAR2 & NA  \\\\\n",
       "\t201 & ABP1 & NA  \\\\\n",
       "\t1 & ACT1 & date\\\\\n",
       "\t2 & ADA2 & date\\\\\n",
       "\t204 & AFG3 & NA  \\\\\n",
       "\t205 & AFR1 & NA  \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 2\n",
       "\n",
       "| <!--/--> | Protein &lt;fct&gt; | HubType &lt;chr&gt; |\n",
       "|---|---|---|\n",
       "| 200 | AAR2 | NA   |\n",
       "| 201 | ABP1 | NA   |\n",
       "| 1 | ACT1 | date |\n",
       "| 2 | ADA2 | date |\n",
       "| 204 | AFG3 | NA   |\n",
       "| 205 | AFR1 | NA   |\n",
       "\n"
      ],
      "text/plain": [
       "    Protein HubType\n",
       "200 AAR2    NA     \n",
       "201 ABP1    NA     \n",
       "1   ACT1    date   \n",
       "2   ADA2    date   \n",
       "204 AFG3    NA     \n",
       "205 AFR1    NA     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(graph_vertices_df_sorted)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>1344</li>\n",
       "\t<li>2</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1344\n",
       "\\item 2\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1344\n",
       "2. 2\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1344    2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dim(graph_vertices_df_sorted)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use `which` in order to find the index numbers of the proteins that are \"date hubs\" and that are \"party hubs\":"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "date_hub_inds <- which(graph_vertices_df_sorted$HubType==\"date\")\n",
    "party_hub_inds <- which(graph_vertices_df_sorted$HubType==\"party\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a sanity check, print out the number of date hubs and party hubs that you find"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"number of date hubs: 91\"\n",
      "[1] \"number of party hubs: 108\"\n"
     ]
    }
   ],
   "source": [
    "print(sprintf(\"number of date hubs: %d\", length(date_hub_inds)))\n",
    "print(sprintf(\"number of party hubs: %d\", length(party_hub_inds)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's use the `transitivity` function in igraph to compute the local clustering coefficients for every vertex in the graph. You'll want to specify `type=\"local\"` in your call to `transitivity`. Print out the first six components of the vector of data returned, as a sanity check.  Question:  why are some of them `NaN`?  Is this normal?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>NaN</li>\n",
       "\t<li>0.666666666666667</li>\n",
       "\t<li>0.0514705882352941</li>\n",
       "\t<li>0.681318681318681</li>\n",
       "\t<li>NaN</li>\n",
       "\t<li>0</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item NaN\n",
       "\\item 0.666666666666667\n",
       "\\item 0.0514705882352941\n",
       "\\item 0.681318681318681\n",
       "\\item NaN\n",
       "\\item 0\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. NaN\n",
       "2. 0.666666666666667\n",
       "3. 0.0514705882352941\n",
       "4. 0.681318681318681\n",
       "5. NaN\n",
       "6. 0\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1]        NaN 0.66666667 0.05147059 0.68131868        NaN 0.00000000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "local_clust_coeffs <- transitivity(ppi_graph, type=\"local\")\n",
    "head(local_clust_coeffs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the histograms of the local clustering coefficients of the \"date hubs\" and the \"party hubs\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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8Yoig4+d5iZmbls2bLK3wMAUBWUHnYZGRl//etfD3nVAw888N3vfre8J5Wu+Iuu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\nEAlhBwAQib8B2ZjBGXl1SlkAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title “”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      },
      "text/plain": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "nbreaks <- 10\n",
    "breaks <- (0:nbreaks)/nbreaks\n",
    "hist_date <- hist(local_clust_coeffs[date_hub_inds], breaks=breaks, plot=FALSE)\n",
    "hist_party <- hist(local_clust_coeffs[party_hub_inds], breaks=breaks, plot=FALSE)\n",
    "plotvals <- 0.5*(breaks[1:nbreaks] + breaks[2:(nbreaks+1)])\n",
    "plot(hist_date, col=rgb(0,0,1,1/4), xlab=expression(C[i]), main=\"\", freq=FALSE)\n",
    "plot(hist_party, col=rgb(0,1,0,1/4), add=TRUE, freq=FALSE)\n",
    "legend(0.3, 2, bty=\"n\", legend=c(\"date\",\"party\"), fill=c(rgb(0,0,1,1/4),rgb(0,1,0,1/4)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's compare these two histograms by a Kolmogorov-Smirnov test, using the `ks.test` function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in ks.test(local_clust_coeffs[date_hub_inds], local_clust_coeffs[party_hub_inds]):\n",
      "“cannot compute exact p-value with ties”\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\tTwo-sample Kolmogorov-Smirnov test\n",
      "\n",
      "data:  local_clust_coeffs[date_hub_inds] and local_clust_coeffs[party_hub_inds]\n",
      "D = 0.26241, p-value = 0.002224\n",
      "alternative hypothesis: two-sided\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(ks.test(local_clust_coeffs[date_hub_inds],\n",
    "              local_clust_coeffs[party_hub_inds]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is the *p*-value for this test?  What conclusion do you draw from that *p*-value?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When comparing two distributions, it is convenient to use a q-q (quantile-quantile) plot.  In R, you can do this using the built-in function `qqplot`. Let's do this for the distributions of Ci values for date hubs and party hubs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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x0KMBv7/jdY7aWAchCS0nbSZXZizU+X2fJItZcCykFISksvskTe6cH1GQLwLAhJ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\niB5CynnqaL0JL1kFZeghpBN0SN5ZEsnxqAB30ENILG6cfWNpMoj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z2919147T75/okw2RFe2bslF53iB4fvYCVRR06j23+efmfCK9mPuW\n9/3vD3vIvhlOYp5Iu3f+7SRfgLsP7RUyv+TOkLj9/okOqSf9Zfv6J/XK8wbB8y+lLlfFTJ3r\n/OuektSndk/9osr8rFWo/Un9Zobrqsz/F/V13H5cyPySu0Li9fsnOqT11J9J//2x/RHISE65\n+wY15rdWCUkRM3Pu88vEnf6+b/4v6GnbnZpV1Eal+csFSn8Kf/OPETO/xBES398/0SFZ21LL\nF5pRe9tuEsXffYMa8x+n4q1kF1WZXyYupPvmz2pINZ98xFDyuErz/+pn7jiyncn/NzHzSxwh\n8f39E/5au1tTE0IT7K8RdPwi3b5BjfnX5zxGOa3K/DJxId0///UXGgTHPinmPyO5zX9sYJWA\nqk+cEDU/uyckXr9/eBsFAAcICYADhATAAUIC4AAhAXCAkAA4QEgAHCAkAA4QEgAHCAmAA4QE\nwAFCAuAAIQFwgJAAOEBIABwgJAAOEBIABwgJgAOEBMABQgLgACEBcICQADhASAAcICQADhAS\nAAcICYADhATAAUIC4AAhAXCAkAA4QEgAHCAkAA4QEgAHCEkLGuf3M7c39ynrX6HdOkUXA7lB\nSFpwT0iraUWuw6yjyVC1a30TjbR9E09JAlYGDghJC/IZ0mSKlT7r/nCs9HOEJBRC0oL8hfSX\nudQV+84Bqs1Y8vl05RcG2RCSZzvYrUyZR4/bQ9r9aLRfdI+9jLWSPoQ9mbHMmQnB5Z8+lzN2\nAs117PWMv8CG0A1VVqxTCMmj/RxsbN6/bKlytpD+KuLb9cm6prCzbO1oGrY0jaU3poeGNaZy\np7IHt6Dzd/xThCQUQvJk1trGrxi70YKipAdAX9tueZuWZ9+1e4Om2b4uop7Zo8sG3vlvEZJQ\nCMmTbaPHpM0fUkjrF1tsu2tpXnZI0THSDayx3y15cJaxyp3/FiEJhZA82Qr6yL4tJZ9suLFl\nTlxOSNepwQpJa9rnGB0Wdue/RUhCISRPNpfW2Ld1bCGlPF3VaKj6SE5IByjbFsfo+nTZsffj\nqCSEJBZC8mSf0hL7towtpA7U5/Mr7LeckC7R4HtGD3b8/WKsC21ASGIhJE+2k/pImyOGKHbN\np5O0u+r2Y6TiNexjPluQPfpXKnvTvnMy0P8WQhILIXm0usbvGLuVSFHsIrW3fX+tLr0qhST9\n6ZlEb9m+/mbunjO6Pz141LY51YhewWMkwRCSR/sl2PjI4AeCpSdkm1GrySPCW/tEfcDWUp0Z\nqexaNWoyuqdfqeM5o9O6kqlajyaB1MWCkARDSJ7tYNeoUt12vTuAsQuDyhRptpgtazCN3ero\nH3aZsZsTHgyMefKfO4d/2bGUX0y71dIuQhIKIQFwgJAAOEBIABwgJAAOEBIABwgJgAOEBMAB\nQgLgACEBcICQADhASAAcICQADhASAAcICYADhATAAUIC4AAhAXCAkAA4QEgAHCAkAA4QEgAH\nCAmAA4QEwAFCAuAAIQFwgJAAOEBIABwgJAAOEBIABwgJgAOEBMDB/wOPfHuciXOAjgAAAABJ\nRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      },
      "text/plain": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "qqplot(local_clust_coeffs[date_hub_inds],local_clust_coeffs[party_hub_inds],xlab=\"date Ci\",ylab=\"party Ci\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "ci_values_date_hubs <- local_clust_coeffs[date_hub_inds]\n",
    "ci_values_party_hubs <- local_clust_coeffs[party_hub_inds]"
   ]
  }
 ],
 "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": 1
}