sitc/sna/4_Social_Networks.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "![](images/EscUpmPolit_p.gif \"UPM\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "# Course Notes for Learning Intelligent Systems"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Department of Telematic Engineering Systems, Universidad Politécnica de Madrid, © Carlos A. Iglesias"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "## [Introduction to  Network Analysis](0_Intro_Network_Analysis.ipynb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Social Networks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# from networkx documentation\n",
    "# Plot degree distribution \n",
    "\n",
    "import collections\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# We convert first the graph from directed to undirected\n",
    "\n",
    "def plot_degree_histogram(G):\n",
    "    degree_sequence = sorted([d for n, d in G.degree()], reverse=True)  # degree sequence\n",
    "    # print \"Degree sequence\", degree_sequence\n",
    "    degreeCount = collections.Counter(degree_sequence)\n",
    "    deg, cnt = zip(*degreeCount.items())\n",
    "    fig, ax = plt.subplots()\n",
    "    plt.bar(deg, cnt, width=0.80, color='b')\n",
    "    plt.title(\"Degree Histogram\")\n",
    "    plt.ylabel(\"Count\")\n",
    "    plt.xlabel(\"Degree\")\n",
    "    ax.set_xticks([d + 0.4 for d in deg])\n",
    "    ax.set_xticklabels(deg)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Regular graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# from Think Complexity\n",
    "def adjacent_edges(nodes, halfk):\n",
    "    n = len(nodes)\n",
    "    for i, u in enumerate(nodes):\n",
    "        for j in range(i+1, i+halfk+1):\n",
    "            v = nodes[j % n]\n",
    "            yield u, v\n",
    "        \n",
    "def make_ring_lattice(n, k):\n",
    "    G = nx.Graph()\n",
    "    nodes = range(n)\n",
    "    G.add_nodes_from(nodes)\n",
    "    G.add_edges_from(adjacent_edges(nodes, k//2))\n",
    "    return G\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "L = make_ring_lattice(10,4)\n",
    "pos = nx.circular_layout(L)\n",
    "nx.draw_networkx(L, pos=pos, with_labels=True, node_size=300, node_color='pink')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.6666666666666667"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Average shortest path\n",
    "nx.average_shortest_path_length(L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_degree_histogram(L)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Erdős–Rényi Random Graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.23025850929940456"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 10\n",
    "p1 = np.log(n) / n\n",
    "p1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgQAAAGFCAYAAACCBut2AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8fJSN1AAAACXBIWXMAAA9hAAAPYQGoP6dpAABKY0lEQVR4nO3deVxUZcM+8GsAUZQll3JJK40l3HAvS81thlFQEBQVF0g0FBWVHvEjvD/wVcr0IQsVFVQUVFwCFBRkScMUyyVJCUVwezQ1UwshVBY5vz/Gp7dVQGbmnmGu7z98PsM5cy44wzkXM/e5j0ySJAlERERk0IxEByAiIiLxWAiIiIiIhYCIiIhYCIiIiAgsBERERAQWAiIiIgILAREREQEwqc1C1dXVuHXrFiwsLCCTyTSdiYiIiNRAkiSUlpaiXbt2MDJ69nsAtSoEt27dQocOHdQSjoiIiLTrxo0baN++/TOXqVUhsLCw+O0JLS0t65+MiIiINK6kpAQdOnT47Tz+LLUqBP/9mMDS0pKFgIiISM/U5uN+DiokIiIiFgIiIiJiISAiIiKwEBARERFYCIiIiAgsBERERAQWAiIiIgILAREREYGFgIiIiMBCQERERGAhICIiIrAQEBEREVgIiIiICCwEREREBBYCIiIiAgsBERERgYWAiIiIwEJAREREYCEgIiIisBAQERERWAiIiIgIgInoAETCSRJQfh+o+hUwMQcatwRkMtGpSNO434n+gIWADFdFMXAlFihcA/x6+f8eN38dsJ0LdPICTF8QlY40hfud6G/JJEmSalqopKQEVlZWePDgASwtLbWRi0izbmUAx9yBqodPH/j9n8HT/xJNmgIDEoF2jtpOR5rC/U4Gpi7nb44hIMNzKwM44gRUPYLqhPDnTvz0sapHquVuZWg/I6kf9zvRM7EQkGGpKFb9hyhJAKprWLhatdwxd9V6pL+434lqxEJAhuVK7NO3i2s6KfxXtWr5q3GaTEWaxv1OVCMWAjIckqQaSPY8Lq5++t8l6R3ud6JaYSEgw1F+/+mo8roe4CXVehU/ayIVaRr3O1GtsBCQ4aj6tX7rV5aqJwdpF/c7Ua2wEJDhMDGv3/qNLNSTg7SL+52oVlgIyHA0bqmafAZ1nY1OplrPtIUmUpGmPed+l7jfycCwEJDhkMlUM9E9Dzt/Tmurr55zv0uShCKjEdzvZDBYCMiwdPJSzURX65e+kWr5jlM1mYo0rY77XYIMjyuN0Hf8Wri5ueHy5cs1r0Sk51gIyLCYvqCallYmQ80vfyPVcgOTOLe9vqvjfpfJjNBEnop1G3fg1KlT6Ny5MwIDA/HgwQMthCUSg4WADE87R+DdVMDEDKrPlf/8lvDTx0zMgMFpQFuF9jOS+tVxvxu9rISnpycuXryI//mf/0FkZCRsbGwQFRWFqqoq7ecn0jAWAjJM7RwB1x+A3p8B5p3++D3zTqrHXW+yDDQ0z7HfmzZtiv/3//4fCgsLMWLECMycORO9evXCoUOHtBqdSNN4t0MiSVJNPlNZqrrEzLQFB5IZgufc76dOncL8+fNx/PhxjBo1CuHh4bC1tdVCYKK6490OiepCJnt6adprqq8sA4bhOfd73759cezYMezevRvnzp1Dly5dEBAQgF9++UWzeYk0jIWAiKiOZDIZPDw8cOHCBSxduhQbN26EjY0NIiMjOb6A9BYLARHRczIzM8PixYtRWFgIFxcXzJ07Fw4ODsjIyBAdjajOWAiIiOqpbdu22Lx5M06fPo1WrVpBqVRi5MiRuHDhguhoRLXGQkBEpCa9evVCdnY2EhMTUVBQgG7dusHf3x/3798XHY2oRiwERERqJJPJ4ObmhgsXLuCjjz7C1q1bYWNjg4iICFRWVoqOR/SPWAiIiDSgcePGCAwMRFFREcaNG4eAgAB069YNqampqMXV3kRax0JARKRBrVu3RlRUFM6cOYOXX34Zzs7OcHR0xPfffy86GtEfsBAQEWmBg4MDvvjiCyQnJ+Pq1atwcHCAn58f7t69KzoaEQAWAiIirZHJZBg9ejTy8/Px73//G/Hx8bCxscGqVatQUVEhOh4ZOBYCIiItMzU1RUBAAIqKijBp0iQsXLgQXbp0QXJyMscXkDAsBEREgrz44ouIjIzE2bNn0alTJ7i6umLYsGE4e/as6GhkgFgIiIgE69q1K9LT05Gamopbt26hZ8+eeP/993Hnzh3R0ciAsBAQEekAmUyGkSNHIi8vD5999hkSEhJgY2ODlStXory8XHQ8MgAsBEREOqRRo0bw9/fHpUuX8N577yEoKAj29vZITEzk+ALSKBYCIiId1KJFC0RERCAvLw/29vYYO3YsBg8ejDNnzoiORg0UCwERkQ6zt7dHamoq0tPTce/ePfTp0wfTpk3D7du3RUejBoaFgIhIDzg6OuLs2bNYu3YtUlJSYGNjg48++giPHj0SHY0aCBYCIiI9YWJiAj8/PxQVFcHX1xehoaF44403sHv3bo4voHpjISAi0jPNmzfHJ598gvz8fPTo0QMTJkzAgAEDcOrUKdHRSI+xEBAR6SlbW1skJyfjiy++QGlpKfr164epU6fi5s2boqORHmIhICLSc8OGDUNubi6ioqKQnp4OW1tbLF26FA8fPhQdjfQICwERUQNgbGyM999/H0VFRZgzZw4+/PBD2NnZYceOHaiurhYdj/QACwERUQNiZWWFFStW4Pz58+jXrx8mT56Mt99+G998843oaKTjWAiIiBqg119/HYmJifjyyy9RXl6O/v37w9PTE9evXxcdjXQUCwERUQM2ePBgnD59Gps3b8bhw4dhZ2eHkJAQ/Prrr6KjkY5hISAiauCMjY0xbdo0FBUVISAgACtXroStrS1iY2M5voB+w0JARGQgLCws8OGHH6KgoAADBw6Et7c33nzzTRw7dkx0NNIBLARERAbmtddew+7du3H06FEAwMCBA+Hh4YGrV68KTkYisRAQERmoAQMG4MSJE4iNjUVOTg7s7e0RFBSE0tJS0dFIABYCIiIDZmRkhKlTp6KwsBCLFi3Cp59+ChsbG2zevBlPnjwRHY+0iIWAiIjQrFkz/O///i8uXryIYcOGYfr06ejTpw+ys7NFRyMtYSEgIqLfvPLKK9ixYweOHz+Oxo0bY8iQIXBzc8Ply5dFRyMNYyEgIqK/6N+/P44fP44dO3bg1KlT6Ny5MwIDA/HgwQPR0UhDWAiIiOhvGRkZwdPTExcvXkRwcDAiIyNhY2ODqKgoji9ogFgIiIjomZo2bYqQkBAUFhZixIgRmDlzJnr27IlDhw6JjkZqxEJARES18vLLLyM2NhYnT56EhYUFhg8fjtGjR6OwsFB0NFIDFgIiIqqTvn374tixY9i9ezfOnTuHLl26ICAgAL/88ovoaFQPLARERFRnMpkMHh4euHDhAv73f/8X0dHRsLGxwbp161BVVSU6Hj0HFgIiInpuZmZmCAoKQlFREVxcXDBnzhw4ODggIyNDdDSqIxYCIiKqt7Zt22Lz5s04ffo0WrVqBaVSiZEjR+LChQuio1EtsRAQEZHa9OrVC9nZ2UhMTERBQQG6desGf39/3L9/X3Q0qgELgbZIEvD4HvDrNdVXSRKdiIhII2QyGdzc3HDhwgV89NFH2Lp1K2xsbLB69WpUVlbW/AQ8Xgohk6Saf9MlJSWwsrLCgwcPYGlpqY1cDUdFMXAlFihcA/z6u6k/zV8HbOcCnbwA0xdEpSMi0rg7d+4gJCQEmzZtgo2NDT755BOMHDkSMpnsjwvyeKl2dTl/sxBo0q0M4Jg7UPXw6QO//1U//UMwaQoMSATaOWo7HRGRVp09exYBAQE4fPgw5HI5Vq1aha5du6q+yeOlRtTl/M2PDDTlVgZwxAmoegTVC/vPvevpY1WPVMvd4ohcImrYHBwc8MUXXyA5ORlXr16Fg4MD/Pz8UHxhN4+XOoCFQBMqilVNV5IAVNewcLVquWPuqvWIiBowmUyG0aNHIz8/H//+97+RuncHTL6egOrqavB4KRYLgSZciX36tldNL+7/qlYtfzVOk6mIiHSGqakpAgICkH8gEM0
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## n: number of nodes and p: probability\n",
    "\n",
    "ER1 = nx.erdos_renyi_graph(n, 0.1)\n",
    "\n",
    "pos = nx.circular_layout(ER1)\n",
    "nx.draw_networkx(ER1, pos=pos, with_labels=False, node_size=100, node_color='orange')\n",
    "nx.is_connected(ER1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjcAAAHHCAYAAABDUnkqAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8fJSN1AAAACXBIWXMAAA9hAAAPYQGoP6dpAAAzZUlEQVR4nO3de3QUVb728achIcEk3YCYBJIAEZgACkGCYgcVwWBEYMi4vBzGYwILOI4Cgoy3qIjAOBmHQfGCAuMRPGIGBpTLQi6GIKASR+4CRxjxwk0SQKCbRGggqfcPX/rYJgESklSy+X7WqiW1a1fVr3pVpx+rdnU7LMuyBAAAYIh6dhcAAABQlQg3AADAKIQbAABgFMINAAAwCuEGAAAYhXADAACMQrgBAABGIdwAAACjEG4AAIBRCDcAjOZwOPT888/bXQaAGkS4AeqAWbNmyeFw+KfQ0FA1b95cqampevXVV3XixAm7S6wRzz//vBwOh44cOVLm8latWqlfv36XvJ/s7GxNmTLlkrcDwB5BdhcA4OJNmDBB8fHxOnPmjPLz87V69WqNHj1aL730khYvXqxOnTrZXWKtc/LkSQUFVexPXXZ2trZv367Ro0dXT1EAqhXhBqhD+vTpo65du/rnMzMztWrVKvXr10+//e1v9dVXX6lhw4Y1Vo9lWTp16lSN7rOiQkND7S6hwoqKihQWFmZ3GUCdxW0poI7r1auXxo4dqz179mj27NkBy3bu3Km7775bTZo0UWhoqLp27arFixeX2saXX36pHj16qGHDhoqNjdWf/vQnzZw5Uw6HQ99//72/37nbPitWrFDXrl3VsGFDTZ8+XZJ0/PhxjR49WnFxcQoJCVGbNm304osvqqSkJGBfJSUlmjJliq655hqFhoYqKipKDz74oI4dO1b1L45Kj7k5ceKERo8erVatWikkJESRkZHq3bu3Nm3aJEm69dZb9eGHH2rPnj3+24CtWrXyr3/o0CENGTJEUVFRCg0NVWJiot55551S+/3xxx/1wAMPyOl0qlGjRsrIyNDWrVvlcDg0a9Ysf79BgwYpPDxc33zzje68805FRETo/vvvlyR98sknuueee9SiRQuFhIQoLi5Ojz76qE6ePBmwr3Pb2Lt3r/r166fw8HDFxMRo6tSpkqRt27apV69eCgsLU8uWLZWdnV1Fry5QO3HlBjDAAw88oKefflofffSRhg0bJknasWOHunfvrpiYGD311FMKCwvTP//5T6Wlpen999/X7373O0nSgQMH1LNnTzkcDmVmZiosLExvvfWWQkJCytzXrl27NHDgQD344IMaNmyYEhIS9NNPP6lHjx46cOCAHnzwQbVo0ULr1q1TZmamDh48GDB+5cEHH9SsWbM0ePBgPfLII/ruu+/0+uuva/Pmzfrss88UHBx8weM9evRome2/DlJl+cMf/qD58+drxIgR6tChg3788Ud9+umn+uqrr9SlSxc988wz8ng82r9/v15++WVJUnh4uKSfb3Hdeuut2r17t0aMGKH4+HjNmzdPgwYN0vHjxzVq1Ch/Hf3799cXX3yhhx56SO3atdOiRYuUkZFRZk1nz55VamqqbrrpJv3tb3/TFVdcIUmaN2+efvrpJz300EO68sor9cUXX+i1117T/v37NW/evIBtFBcXq0+fPrrlllv017/+Ve+9955GjBihsLAwPfPMM7r//vt11113adq0aUpPT5fb7VZ8fPwFXy+gTrIA1HozZ860JFnr168vt4/L5bKuu+46//xtt91mdezY0Tp16pS/raSkxEpOTrbatm3rbxs5cqTlcDiszZs3+9t+/PFHq0mTJpYk67vvvvO3t2zZ0pJkLV++PGDfEydOtMLCwqx///vfAe1PPfWUVb9+fWvv3r2WZVnWJ598Ykmy3nvvvYB+y5cvL7P918aNG2dJOu/Ut2/fgHUkWePGjQt4nYYPH37e/fTt29dq2bJlqfYpU6ZYkqzZs2f7206fPm253W4rPDzc8nq9lmVZ1vvvv29JsqZMmeLvV1xcbPXq1cuSZM2cOdPfnpGRYUmynnrqqVL7++mnn0q1ZWVlWQ6Hw9qzZ0+pbfz5z3/2tx07dsxq2LCh5XA4rDlz5vjbd+7cWeo1AUzDbSnAEOHh4f6npo4ePapVq1bp3nvv1YkTJ3TkyBEdOXJEP/74o1JTU/X111/rwIEDkqTly5fL7Xarc+fO/m01adLEf2vk1+Lj45WamhrQNm/ePN18881q3Lixf19HjhxRSkqKiouLtXbtWn8/l8ul3r17B/RLSkpSeHi4Pv7444s61vfff185OTmlpqioqAuu26hRI/3rX//SDz/8cFH7+qWlS5cqOjpaAwcO9LcFBwfrkUceUWFhodasWSPp59c0ODjYfxVNkurVq6fhw4eXu+2HHnqoVNsvxzIVFRXpyJEjSk5OlmVZ2rx5c6n+Q4cO9f+7UaNGSkhIUFhYmO69915/e0JCgho1aqRvv/32Io8aqHu4LQUYorCwUJGRkZKk3bt3y7IsjR07VmPHji2z/6FDhxQTE6M9e/bI7XaXWt6mTZsy1yvrVsbXX3+tL7/8UldddVW5+zrXz+Px+Ossr9+F3HLLLWratGmp9osZPPzXv/5VGRkZiouLU1JSku68806lp6fr6quvvuC6e/bsUdu2bVWvXuD/F7Zv396//Nx/mzVr5r+9dE55r2lQUJBiY2NLte/du1fPPfecFi9eXGpMksfjCZgPDQ0t9fq7XC7FxsbK4XCUaq+uMU5AbUC4AQywf/9+eTwe/4fnubEnjz32WKmrLOeU90F7IWU9GVVSUqLevXvriSeeKHOd3/zmN/5+kZGReu+998rsV144qkr33nuvbr75Zi1YsEAfffSRJk2apBdffFEffPCB+vTpU+37L0tISEipwFRcXKzevXvr6NGjevLJJ9WuXTuFhYXpwIEDGjRoUKnxRfXr1y9z2+W1W5ZVNcUDtRDhBjDAu+++K0n+IHPuKkRwcLBSUlLOu27Lli21e/fuUu1ltZWndevWKiwsvOC+WrdurZUrV6p79+62Pj7erFkzPfzww3r44Yd16NAhdenSRS+88II/3Pz6Ssc5LVu21JdffqmSkpKAMLJz507/8nP//fjjj/XTTz8FXL2pyGu6bds2/fvf/9Y777yj9PR0f3tOTs7FHyhwmWLMDVDHrVq1ShMnTlR8fLx/nExkZKRuvfVWTZ8+XQcPHiy1zuHDh/3/Tk1NVV5enrZs2eJvO3r0aLlXV8py7733Ki8vTytWrCi17Pjx4zp79qy/X3FxsSZOnFiq39mzZ3X8+PGL3mdlFBcXl7qdExkZqebNm8vn8/nbwsLCSvWTpDvvvFP5+fmaO3euv+3s2bN67bXXFB4erh49ekj6+TU9c+aM/v73v/v7lZSU+B/Nvhjnrrj88gqLZVl65ZVXLnobwOWKKzdAHbJs2TLt3LlTZ8+eVUFBgVatWqWcnBy1bNlSixcvDhhzMnXqVN10003q2LGjhg0bpquvvloFBQXKy8vT/v37tXXrVknSE088odmzZ6t3794aOXKk/1HwFi1a6OjRo+Vexfilxx9/XIsXL1a/fv00aNAgJSUlqaioSNu2bdP8+fP1/fffq2nTpurRo4cefPBBZWVlacuWLbr99tsVHBysr7/+WvPmzdMrr7yiu+++u9pevxMnTig2NlZ33323EhMTFR4erpUrV2r9+vWaPHmyv19SUpLmzp2rMWPG6Prrr1d4eLj69++v//qv/9L06dM1aNAgbdy4Ua1atdL8+fP12WefacqUKYqIiJAkpaWl6YYbbtAf//hH7d69W+3atdPixYv9j7BfzGvarl07tW7dWo899pgOHDggp9Op999/n7EywMWw9VktABfl3KPg56YGDRpY0dHRVu/eva1XXnnF/wjyr33zzTdWenq6FR0dbQUHB1sxMTFWv379rPnz5wf027x5s3XzzTdbISEhVmxsrJWVlWW9+uqrliQrPz/f369ly5alHrU+58SJE1ZmZqbVpk0bq0GDBlbTpk2t5ORk629/+5t1+vTpgL4zZsywkpKSrIYNG1o
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_degree_histogram(ER1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ER2 = nx.erdos_renyi_graph(10, 0.6) \n",
    "\n",
    "pos = nx.circular_layout(ER1)\n",
    "nx.draw_networkx(ER2, pos=pos, with_labels=False, node_size=100, node_color='orange')\n",
    "nx.is_connected(ER2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_degree_histogram(ER2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Small world. Watts-Strogatz (WS) graphs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 700x225 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(7, 2.25))\n",
    "for i, p in enumerate([0.0, 0.1, 1.0]):\n",
    "    # Generate the graph: n: number of nodes;  k: neighbours, p: prob of rewiring an edge\n",
    "    G = nx.watts_strogatz_graph(8, 4, p)\n",
    "    # Create layout and draw\n",
    "    plt.subplot(1, 3, i + 1)\n",
    "    pos = nx.circular_layout(G)\n",
    "    nx.draw_networkx(G, pos=pos, node_color='pink')\n",
    "    plt.title(\"p = {:0.1f}\".format(p))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_degree_histogram(G)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Barabasi-Albert Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G_preferential_35 = nx.barabasi_albert_graph(35, 1)\n",
    "pos = nx.spring_layout(G_preferential_35, k=0.1)\n",
    "nx.draw_networkx(G_preferential_35, pos, node_color='pink')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjIAAAHHCAYAAACle7JuAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8fJSN1AAAACXBIWXMAAA9hAAAPYQGoP6dpAAAs80lEQVR4nO3de1RVdf7/8dcREIjLIVRuooiX0EwptPyilnlFS7+pU5bjJDjpOAYWmVnUz9QsmWpqrMbU6pu2TNPRspwmNe/dLC/lrUkT867gLa4qKuzfHy3PikAFBPb50POx1ll59tlnn/c+ueLZPntzHJZlWQIAADBQHbsHAAAAqCxCBgAAGIuQAQAAxiJkAACAsQgZAABgLEIGAAAYi5ABAADGImQAAICxCBkAAGAsQgZAreJwODRx4kS7xwBQQwgZwA3Nnj1bDofDdfPx8VFERIQSEhL06quvKi8vz+4Ra8TEiRPlcDh04sSJMh9v0qSJ+vbte9WvM2/ePE2dOvWqtwOg5nnaPQCAS3vmmWcUHR2t8+fPKzMzU2vXrlVqaqpefvllLVmyRG3btrV7RLdz5swZeXpW7D9t8+bN044dO5Samlo9QwGoNoQM4Mb69Omj9u3bu+6npaVp9erV6tu3r/73f/9XP/zwg3x9fWtsHsuydPbs2Rp9zYry8fGxe4QKKygokJ+fn91jAEbioyXAMN26ddP48eO1f/9+vfvuuyUe27lzp+6++24FBwfLx8dH7du315IlS0ptY9u2berSpYt8fX0VGRmpZ599VrNmzZLD4dC+fftc61386Gb58uVq3769fH19NXPmTElSdna2UlNT1ahRI3l7e6t58+Z6/vnnVVxcXOK1iouLNXXqVLVu3Vo+Pj4KDQ3VyJEj9fPPP1f9m6PS58jk5eUpNTVVTZo0kbe3t0JCQtSzZ099++23kqTbb79d//nPf7R//37XR3lNmjRxPf/YsWN64IEHFBoaKh8fH8XGxuqdd94p9bonT57U/fffr8DAQAUFBSkxMVFbt26Vw+HQ7NmzXeslJSXJ399fe/bs0R133KGAgAANGTJEkvT555/rnnvuUePGjeXt7a1GjRrpkUce0ZkzZ0q81sVtHDhwQH379pW/v78aNmyoadOmSZK2b9+ubt26yc/PT1FRUZo3b14VvbuA++GIDGCg+++/X08++aQ+/fRTjRgxQpL0/fffq1OnTmrYsKGeeOIJ+fn56V//+pf69++v999/XwMGDJAkHT58WF27dpXD4VBaWpr8/Pz01ltvydvbu8zX2rVrlwYPHqyRI0dqxIgRiomJ0enTp9WlSxcdPnxYI0eOVOPGjfXVV18pLS1NR48eLXG+yciRIzV79mwNGzZMDz30kPbu3at//vOf+u677/Tll1/Ky8vrivt76tSpMpf/NprK8te//lWLFi1SSkqKrr/+ep08eVJffPGFfvjhB8XFxempp55STk6ODh06pH/84x+SJH9/f0m/fEx1++23KyMjQykpKYqOjtbChQuVlJSk7OxsPfzww645+vXrpw0bNmjUqFFq2bKlPvroIyUmJpY504ULF5SQkKDOnTvr73//u6655hpJ0sKFC3X69GmNGjVK9erV04YNG/Taa6/p0KFDWrhwYYltFBUVqU+fPrrtttv0wgsvaO7cuUpJSZGfn5+eeuopDRkyRAMHDtSMGTM0dOhQxcfHKzo6+orvF2AcC4DbmTVrliXJ2rhx4yXXcTqd1k033eS63717d6tNmzbW2bNnXcuKi4utjh07Wi1atHAtGz16tOVwOKzvvvvOtezkyZNWcHCwJcnau3eva3lUVJQlyVq2bFmJ1548ebLl5+dn/fjjjyWWP/HEE5aHh4d14MABy7Is6/PPP7ckWXPnzi2x3rJly8pc/lsTJkywJF32duedd5Z4jiRrwoQJJd6n5OTky77OnXfeaUVFRZVaPnXqVEuS9e6777qWnTt3zoqPj7f8/f2t3Nxcy7Is6/3337ckWVOnTnWtV1RUZHXr1s2SZM2aNcu1PDEx0ZJkPfHEE6Ve7/Tp06WWpaenWw6Hw9q/f3+pbUyZMsW17Oeff7Z8fX0th8NhzZ8/37V8586dpd4ToDbhoyXAUP7+/q6rl06dOqXVq1dr0KBBysvL04kTJ3TixAmdPHlSCQkJ2r17tw4fPixJWrZsmeLj43XjjTe6thUcHOz6eOO3oqOjlZCQUGLZwoULdeutt+raa691vdaJEyfUo0cPFRUV6bPPPnOt53Q61bNnzxLrtWvXTv7+/lqzZk259vX999/XihUrSt1CQ0Ov+NygoCB98803OnLkSLle69c++eQThYWFafDgwa5lXl5eeuihh5Sfn69169ZJ+uU99fLych0dk6Q6deooOTn5ktseNWpUqWW/PveooKBAJ06cUMeOHWVZlr777rtS6w8fPtz156CgIMXExMjPz0+DBg1yLY+JiVFQUJB++umncu41YBY+WgIMlZ+fr5CQEElSRkaGLMvS+PHjNX78+DLXP3bsmBo2bKj9+/crPj6+1OPNmzcv83llfRyxe/dubdu2TQ0aNLjka11cLycnxzXnpda7kttuu03169cvtbw8J/a+8MILSkxMVKNGjdSuXTvdcccdGjp0qJo2bXrF5+7fv18tWrRQnTol/5+vVatWrscv/jM8PNz1EdFFl3pPPT09FRkZWWr5gQMH9PTTT2vJkiWlziHKyckpcd/Hx6fU++90OhUZGSmHw1FqeXWdkwTYjZABDHTo0CHl5OS4flBePFdk7NixpY6eXHSpH6pXUtYVSsXFxerZs6fGjRtX5nOuu+4613ohISGaO3dumetdKoSq0qBBg3Trrbdq8eLF+vTTT/Xiiy/q+eef1wcffKA+ffpU++uXxdvbu1QcFRUVqWfPnjp16pQef/xxtWzZUn5+fjp8+LCSkpJKnQ/k4eFR5rYvtdyyrKoZHnAzhAxgoDlz5kiSK1ouHl3w8vJSjx49LvvcqKgoZWRklFpe1rJLadasmfLz86/4Ws2aNdPKlSvVqVMnWy/ZDg8P14MPPqgHH3xQx44dU1xcnJ577jlXyPz2CMZFUVFR2rZtm4qLi0uEx86dO12PX/znmjVrdPr06RJHZSrynm7fvl0//vij3nnnHQ0dOtS1fMWKFeXfUeB3iHNkAMOsXr1akydPVnR0tOu8lpCQEN1+++2aOXOmjh49Wuo5x48fd/05ISFB69ev15YtW1zLTp06dcmjJmUZNGiQ1q9fr+XLl5d6LDs7WxcuXHCtV1RUpMmTJ5da78KFC8rOzi73a1ZGUVFRqY9kQkJCFBERocLCQtcyPz+/UutJ0h133KHMzEwtWLDAtezChQt67bXX5O/vry5dukj65T09f/683nzzTdd6xcXFrsuhy+PikZRfHzmxLEuvvPJKubcB/B5xRAZwY0uXLtXOnTt14cIFZWVlafXq1VqxYoWioqK0ZMmSEueITJs2TZ07d1abNm00YsQINW3aVFlZWVq/fr0OHTqkrVu3SpLGjRund999Vz179tTo0aNdl183btxYp06duuTRiV977LHHtGTJEvXt21dJSUlq166dCgoKtH37di1atEj79u1T/fr11aVLF40cOVLp6enasmWLevXqJS8vL+3evVsLFy7UK6+8orvvvrva3r+8vDxFRkbq7rvvVmxsrPz9/bVy5Upt3LhRL730kmu9du3aacGCBRozZoxuvvlm+fv7q1+/fvrLX/6imTNnKikpSZs3b1aTJk20aNEiffnll5o6daoCAgIkSf3799ctt9yiRx99VBkZGWrZsqWWLFniumy8PO9py5Yt1axZM40dO1aHDx9WYGCg3n//fc5tAa7E1mumAJTp4uXXF29169a1wsLCrJ49e1qvvPKK67Lf39qzZ481dOhQKywszPLy8rIaNmxo9e3b11q0aFGJ9b777jvr1ltvtby9va3IyEgrPT3devXVVy1JVmZmpmu9qKioUpc3X5SXl2elpaVZzZs3t+rWrWvVr1/f6tixo/X3v//dOnfuXIl133jjDatdu3aWr6+vFRAQYLVp08YaN26cdeTIkcu
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_degree_histogram(G_preferential_35)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Example Barabasi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# n = 1000 nodes and m = 2 minimum degree\n",
    "BA = nx.barabasi_albert_graph(1000, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pos = nx.spring_layout(BA)\n",
    "plt.figure(figsize=(6,6))\n",
    "nx.draw(BA, pos, node_color='c', node_size=60, with_labels=False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1000"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# number of nodes\n",
    "BA.order()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1996"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# number of edges´plt.bar(deg, cnt, width=0.80, color='b')\n",
    "BA.size()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.992"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# average degree\n",
    "2*BA.number_of_edges() / float(BA.number_of_nodes())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(2, 90), (5, 86), (4, 68), (0, 60), (7, 33), (10, 32), (29, 30), (9, 27)]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Sorted nodes by degree\n",
    "sorted(BA.degree, key=lambda x: x[1], reverse=True)[0:8]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# node with the largest degree\n",
    "node_highest_degree, degree = sorted(BA.degree, key=lambda x: x[1], reverse=True)[0]\n",
    "node_highest_degree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[3, 4, 6, 7, 11, 13, 14, 17, 23]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# neighbors\n",
    "list(BA.neighbors(node_highest_degree))[1:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "### Ego network\n",
    "EGO_HIGHEST = nx.ego_graph(BA, node_highest_degree)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Draw ego_network\n",
    "os = nx.spring_layout(EGO_HIGHEST)\n",
    "plt.figure(figsize=(6,6))\n",
    "nx.draw(EGO_HIGHEST, pos, node_color='c', node_size=60)\n",
    "nx.draw_networkx_nodes(EGO_HIGHEST, pos, nodelist=[node_highest_degree], node_size=100, node_color=\"r\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_degree_histogram(EGO_HIGHEST)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Ego network 2 hops\n",
    "EGO_HIGHEST_2 = nx.ego_graph(BA, node_highest_degree, radius=4)\n",
    "os = nx.spring_layout(EGO_HIGHEST_2)\n",
    "plt.figure(figsize=(6,6))\n",
    "nx.draw(EGO_HIGHEST_2, pos, node_color='c', node_size=60)\n",
    "nx.draw_networkx_nodes(EGO_HIGHEST_2, pos, nodelist=[node_highest_degree], node_size=100, node_color=\"r\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "## Licence"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "The notebook is freely licensed under under the [Creative Commons Attribution Share-Alike license](https://creativecommons.org/licenses/by/2.0/).  \n",
    "\n",
    "© Carlos A. Iglesias, Universidad Politécnica de Madrid."
   ]
  }
 ],
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