{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "b6535345",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# netowrks\n",
"import networkx as nx\n",
"import igraph as ig\n",
"\n",
"# data processing\n",
"import pandas as pd\n",
"import numpy as np\n",
"\n",
"#some functions to make our lifes easier\n",
"import sys\n",
"sys.path.append(\"./\")\n",
"from common_functions import *\n",
"\n",
"# viz\n",
"import pylab as plt\n",
"import seaborn as sns\n",
"%matplotlib inline\n",
"\n",
"#Change the default options of visualization (improving the defaults)\n",
"custom_params = {\"axes.spines.right\": False, \"axes.spines.top\": False, \"axes.spines.left\": False, \"axes.spines.bottom\":\n",
"False,\"lines.linewidth\": 2, \"grid.color\": \"lightgray\", \"legend.frameon\": False, \"xtick.labelcolor\": \"#484848\", \"ytick.labelcolor\":\n",
"\"#484848\", \"xtick.color\": \"#484848\", \"ytick.color\": \"#484848\",\"text.color\": \"#484848\", \"axes.labelcolor\": \"#484848\",\n",
"\"axes.titlecolor\":\"#484848\",\"figure.figsize\": [5,3],\n",
"\"axes.titlelocation\":\"left\",\"xaxis.labellocation\":\"left\",\"yaxis.labellocation\":\"bottom\"}\n",
"palette = [\"#3d348b\",\"#e6af2e\",\"#191716\",\"#e0e2db\"] #use your favourite colours\n",
"sns.set_theme(context='paper', style='white', palette=palette, font='Verdana', font_scale=1.3, color_codes=True,\n",
"rc=custom_params)\n",
"\n",
"from IPython.display import display, HTML\n",
"display(HTML(\"\"))"
]
},
{
"cell_type": "markdown",
"id": "4767bb68",
"metadata": {},
"source": [
"# Exercise 1: Reading and visualizing graphs"
]
},
{
"cell_type": "markdown",
"id": "9a2566d2",
"metadata": {},
"source": [
"## 1.1. Basic plot\n",
"- Read and understand the following code\n",
"\n",
"(nothing to code!)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "5b408279",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Nodes: ['Acciaiuoli', 'Medici', 'Castellani', 'Peruzzi', 'Strozzi', 'Barbadori', 'Ridolfi', 'Tornabuoni', 'Albizzi', 'Salviati', 'Pazzi', 'Bischeri', 'Guadagni', 'Ginori', 'Lamberteschi']\n",
"Edges: [('Acciaiuoli', 'Medici'), ('Medici', 'Barbadori'), ('Medici', 'Ridolfi'), ('Medici', 'Tornabuoni'), ('Medici', 'Albizzi'), ('Medici', 'Salviati'), ('Castellani', 'Peruzzi'), ('Castellani', 'Strozzi'), ('Castellani', 'Barbadori'), ('Peruzzi', 'Strozzi'), ('Peruzzi', 'Bischeri'), ('Strozzi', 'Ridolfi'), ('Strozzi', 'Bischeri'), ('Ridolfi', 'Tornabuoni'), ('Tornabuoni', 'Guadagni'), ('Albizzi', 'Ginori'), ('Albizzi', 'Guadagni'), ('Salviati', 'Pazzi'), ('Bischeri', 'Guadagni'), ('Guadagni', 'Lamberteschi')]\n"
]
},
{
"data": {
"image/png": 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\n",
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