src/notebooks/327-network-from-correlation-matrix.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose that you have 10 individuals, and know how close they are related to each other. It is possible to represent these **relationships** in a network. Each individual will be a **node**. If 2 individuals are close enough (we set a **threshold**), then they are linked by an **edge**. That will show the structure of the population!\n",
    "\n",
    "In this example, we see that our population is clearly split into 2 groups!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# libraries\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    " \n",
    "# I build a data set: 10 individuals and 5 variables for each\n",
    "ind1=[5,10,3,4,8,10,12,1,9,4]\n",
    "ind5=[1,1,13,4,18,5,2,11,3,8]\n",
    "df = pd.DataFrame({ 'A':ind1, 'B':ind1 + np.random.randint(10, size=(10)) , 'C':ind1 + np.random.randint(10, size=(10)) , 'D':ind1 + np.random.randint(5, size=(10)) , 'E':ind1 + np.random.randint(5, size=(10)), 'F':ind5, 'G':ind5 + np.random.randint(5, size=(10)) , 'H':ind5 + np.random.randint(5, size=(10)), 'I':ind5 + np.random.randint(5, size=(10)), 'J':ind5 + np.random.randint(5, size=(10))})\n",
    " \n",
    "# Calculate the correlation between individuals. We have to transpose first, because the corr function calculate the pairwise correlations between columns.\n",
    "corr = df.corr()\n",
    " \n",
    "# Transform it in a links data frame (3 columns only):\n",
    "links = corr.stack().reset_index()\n",
    "links.columns = ['var1', 'var2', 'value']\n",
    " \n",
    "# Keep only correlation over a threshold and remove self correlation (cor(A,A)=1)\n",
    "links_filtered=links.loc[ (links['value'] > 0.8) & (links['var1'] != links['var2']) ]\n",
    " \n",
    "# Build your graph\n",
    "G=nx.from_pandas_edgelist(links_filtered, 'var1', 'var2')\n",
    " \n",
    "# Plot the network:\n",
    "nx.draw(G, with_labels=True, node_color='orange', node_size=400, edge_color='black', linewidths=1, font_size=15)"
   ]
  }
 ],
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  "description": "This post explains how to draw a <b>correlation network</b>: a <a href='https://python-graph-gallery.com/network-chart/'>network</a> build on a correlation matrix.",
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