diff --git a/src/algo1_testing.ipynb b/src/algo1_testing.ipynb
index f5f94a9..3629dec 100644
--- a/src/algo1_testing.ipynb
+++ b/src/algo1_testing.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -27,7 +27,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -45,7 +45,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -77,7 +77,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -94,7 +94,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -116,7 +116,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -137,7 +137,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -148,7 +148,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -160,7 +160,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -183,7 +183,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -193,7 +193,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -242,116 +242,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": null,
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "tau =  1e-05\n",
-      "The algorithm converged in  19  iterations\n",
-      "The algorithm took  12.630054473876953  seconds\n",
-      "\n",
-      "tau =  1e-06\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/tmp/ipykernel_1733107/908708813.py:13: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.\n",
-      "  df = df.append({'alpha': a, 'iterations': mv, 'tau': tau, 'time': total_time}, ignore_index=True)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "The algorithm converged in  56  iterations\n",
-      "The algorithm took  32.28381681442261  seconds\n",
-      "\n",
-      "tau =  1e-07\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/tmp/ipykernel_1733107/908708813.py:13: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.\n",
-      "  df = df.append({'alpha': a, 'iterations': mv, 'tau': tau, 'time': total_time}, ignore_index=True)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "The algorithm converged in  113  iterations\n",
-      "The algorithm took  75.9386818408966  seconds\n",
-      "\n",
-      "tau =  1e-08\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/tmp/ipykernel_1733107/908708813.py:13: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.\n",
-      "  df = df.append({'alpha': a, 'iterations': mv, 'tau': tau, 'time': total_time}, ignore_index=True)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "The algorithm converged in  275  iterations\n",
-      "The algorithm took  107.68565726280212  seconds\n",
-      "\n",
-      "tau =  1e-09\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/tmp/ipykernel_1733107/908708813.py:13: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.\n",
-      "  df = df.append({'alpha': a, 'iterations': mv, 'tau': tau, 'time': total_time}, ignore_index=True)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "The algorithm converged in  454  iterations\n",
-      "The algorithm took  152.8943109512329  seconds\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/tmp/ipykernel_1733107/908708813.py:13: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.\n",
-      "  df = df.append({'alpha': a, 'iterations': mv, 'tau': tau, 'time': total_time}, ignore_index=True)\n"
-     ]
-    },
-    {
-     "ename": "OSError",
-     "evalue": "Cannot save file into a non-existent directory: '../data/algo1'",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mOSError\u001b[0m                                   Traceback (most recent call last)",
-      "\u001b[0;32m/tmp/ipykernel_1733107/908708813.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     14\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     15\u001b[0m \u001b[0;31m# save the results in a csv file\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 16\u001b[0;31m \u001b[0mdf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mto_csv\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'../data/algo1/different_tau.csv'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mindex\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     17\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m~/.local/lib/python3.10/site-packages/pandas/core/generic.py\u001b[0m in \u001b[0;36mto_csv\u001b[0;34m(self, path_or_buf, sep, na_rep, float_format, columns, header, index, index_label, mode, encoding, compression, quoting, quotechar, line_terminator, chunksize, date_format, doublequote, escapechar, decimal, errors, storage_options)\u001b[0m\n\u001b[1;32m   3549\u001b[0m         )\n\u001b[1;32m   3550\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 3551\u001b[0;31m         return DataFrameRenderer(formatter).to_csv(\n\u001b[0m\u001b[1;32m   3552\u001b[0m             \u001b[0mpath_or_buf\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3553\u001b[0m             \u001b[0mline_terminator\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mline_terminator\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m~/.local/lib/python3.10/site-packages/pandas/io/formats/format.py\u001b[0m in \u001b[0;36mto_csv\u001b[0;34m(self, path_or_buf, encoding, sep, columns, index_label, mode, compression, quoting, quotechar, line_terminator, chunksize, date_format, doublequote, escapechar, errors, storage_options)\u001b[0m\n\u001b[1;32m   1178\u001b[0m             \u001b[0mformatter\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfmt\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1179\u001b[0m         )\n\u001b[0;32m-> 1180\u001b[0;31m         \u001b[0mcsv_formatter\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msave\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1181\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1182\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mcreated_buffer\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m~/.local/lib/python3.10/site-packages/pandas/io/formats/csvs.py\u001b[0m in \u001b[0;36msave\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    239\u001b[0m         \"\"\"\n\u001b[1;32m    240\u001b[0m         \u001b[0;31m# apply compression and byte/text conversion\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 241\u001b[0;31m         with get_handle(\n\u001b[0m\u001b[1;32m    242\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfilepath_or_buffer\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    243\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmode\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m~/.local/lib/python3.10/site-packages/pandas/io/common.py\u001b[0m in \u001b[0;36mget_handle\u001b[0;34m(path_or_buf, mode, encoding, compression, memory_map, is_text, errors, storage_options)\u001b[0m\n\u001b[1;32m    692\u001b[0m     \u001b[0;31m# Only for write methods\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    693\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0;34m\"r\"\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mmode\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mis_path\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 694\u001b[0;31m         \u001b[0mcheck_parent_directory\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mhandle\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    695\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    696\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mcompression\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m~/.local/lib/python3.10/site-packages/pandas/io/common.py\u001b[0m in \u001b[0;36mcheck_parent_directory\u001b[0;34m(path)\u001b[0m\n\u001b[1;32m    566\u001b[0m     \u001b[0mparent\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mPath\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpath\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mparent\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    567\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mparent\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mis_dir\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 568\u001b[0;31m         \u001b[0;32mraise\u001b[0m \u001b[0mOSError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mrf\"Cannot save file into a non-existent directory: '{parent}'\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    569\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    570\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;31mOSError\u001b[0m: Cannot save file into a non-existent directory: '../data/algo1'"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "# list of alpha values, from 0.85 to 0.99 with step 0.01\n",
     "a = []\n",
@@ -371,7 +264,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -388,7 +281,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -430,6 +323,57 @@
     "\n",
     "_In the right folder_"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def Arnoldi(A, v, m): #  defined ad algorithm 2 in the paper\n",
+    "    beta = norm(v)\n",
+    "    print(\"A\")\n",
+    "    v = v/beta\n",
+    "    print(\"B\")\n",
+    "    h = sp.sparse.lil_matrix((m,m))\n",
+    "    print(\"C\")\n",
+    "\n",
+    "    for j in range(1,m):\n",
+    "        w = A.dot(v)\n",
+    "        for i in range(1,j):\n",
+    "            h[i,j] = v.T.dot(w)\n",
+    "            w = w - h[i,j]*v\n",
+    "\n",
+    "        h[j+1,j] = norm(w)\n",
+    "\n",
+    "        if h[j+1,j] == 0:\n",
+    "            m = j\n",
+    "            v[m+1] = 0\n",
+    "            break\n",
+    "        else:\n",
+    "            v = w**h[j+1,j]\n",
+    "\n",
+    "    return v, h, m, beta, j"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "A = sp.sparse.rand(100,100, density=0.5, format='lil')\n",
+    "v = sp.sparse.rand(100,1, density=1, format='lil')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "v, h, m, beta, j = Arnoldi(A, v, 100)"
+   ]
   }
  ],
  "metadata": {
diff --git a/src/main.py b/src/main.py
new file mode 100755
index 0000000..5fed57a
--- /dev/null
+++ b/src/main.py
@@ -0,0 +1,221 @@
+#!/usr/bin/env python3
+
+# Importing the libraries
+import os
+import wget
+import gzip
+import time
+import warnings
+import scipy as sp
+import numpy as np
+import pandas as pd
+import networkx as nx
+import plotly.graph_objs as go
+from scipy.sparse import *
+from scipy.sparse.linalg import norm
+from os.path import exists
+
+
+warnings.simplefilter(action='ignore', category=FutureWarning)
+# some stupid pandas function that doesn't work
+
+class utilities:
+    # Importing the dataset
+    def load_data():
+        # Loading the dataset
+        dataset = int(input("Choose the dataset:\n  [1] web-Stanford\n  [2] web-BerkStan: \nEnter an option: "))
+
+        if dataset == 1:
+            if exists('../data/web-Stanford.txt'):
+                dataset = '../data/web-Stanford.txt'
+            else:
+                print("\nThe file doesn't exist, download it from https://snap.stanford.edu/data/web-Stanford.html")
+
+                # if there is no folder data, create it
+                if not exists('../data'):
+                    os.makedirs('../data')
+
+                # Downloading the dataset
+                url = 'https://snap.stanford.edu/data/web-Stanford.txt.gz'
+                wget.download(url, '../data/web-Stanford.txt.gz')
+                # Unzipping the dataset
+                with gzip.open('../data/web-Stanford.txt.gz', 'rb') as f_in:
+                    with open('../data/web-Stanford.txt', 'wb') as f_out:
+                        f_out.write(f_in.read())
+
+                dataset = '../data/web-Stanford.txt'
+                print("\nDataset downloaded\n")
+
+        elif dataset == 2:
+            if exists('../data/web-BerkStan.txt'):
+                dataset = '../data/web-BerkStan.txt'
+            else:
+                print("\nThe file doesn't exist, download it from https://snap.stanford.edu/data/web-BerkStan.html")
+
+                # if there is no folder data, create it
+                if not exists('../data'):
+                    os.makedirs('../data')
+
+                # Downloading the dataset
+                url = 'https://snap.stanford.edu/data/web-BerkStan.txt.gz'
+                wget.download(url, '../data/web-BerkStan.txt.gz')
+                # Unzipping the dataset
+                with gzip.open('../data/web-BerkStan.txt.gz', 'rb') as f_in:
+                    with open('../data/web-BerkStan.txt', 'wb') as f_out:
+                        f_out.write(f_in.read())
+
+                dataset = '../data/web-BerkStan.txt'
+                print("\nDataset downloaded\n")
+
+        return dataset
+
+    # Creating the graph from the dataset
+    def create_graph(dataset):
+        print("\nCreating the graph...")
+        G = nx.read_edgelist(dataset, create_using=nx.DiGraph(), nodetype=int)
+        n = G.number_of_nodes()
+        print("Graph created based on the dataset\n")
+        return G, n
+
+    # # Creating the transition probability matrix
+    # The matrix is filled with zeros and the (i,j) element is x if the node i is connected to the node j. Where x is 1/(number of nodes connected to i).
+    def create_matrix(G):
+        print("Creating the transition probability matrix...")
+        P = sp.sparse.lil_matrix((n,n))
+        for i in G.nodes():
+            for j in G[i]: #G[i] is the list of nodes connected to i, it's neighbors
+                P[i-1,j-1] = 1/len(G[i])
+        print("Transition probability matrix created\n")
+        return P
+
+    # The vector is filled with d(i) = 1 if the i row of the matrix P is filled with zeros, other wise is 0
+    def dangling_nodes(P,n):
+        print("Creating the list of dangling nodes...")
+        d = sp.sparse.lil_matrix((n,1))
+        for i in range(n):
+            if P[i].sum() == 0:
+                d[i] = 1
+        print("List of dangling nodes created\n")
+        return d
+
+    def probability_vector(n):
+        print("Creating the probability vector...")
+        v = sp.sparse.lil_matrix((n,1))
+        for i in range(n):
+            v[i] = 1/n
+        print("Probability vector created\n")
+        return v
+
+    def transition_matrix(P, v, d):
+        print("Creating the transition matrix...")
+        Pt = P + v.dot(d.T)
+        print("Transition matrix created\n")
+        return Pt
+
+    def alpha():
+        a = []
+        for i in range(85,100):
+            a.append(i/100)
+        return a
+
+class Plotting:
+    def tau_over_iterations(dataframe):
+        dataframe = df
+        x = df['tau'][::-1].tolist()
+        y = df['iterations'].tolist()
+
+        fig = go.Figure(data=go.Scatter(x=x, y=y, mode='lines+markers'),
+                                    layout=go.Layout(title='Iterations needed for the convergence', xaxis_title='tau', yaxis_title='iterations'))
+
+        # save the figure as a html file
+        fig.write_html("../data/results/algo1/taus_over_iterations.html")
+        print("The plot has been saved in the folder data/results/algo1")
+
+    def tau_over_time(df):
+        x1 = df['tau'][::-1].tolist()
+        y1 = df['time'].tolist()
+
+        fig = go.Figure(data=go.Scatter(x=x1, y=y1, mode='lines+markers'),
+                                        layout=go.Layout(title='Time needed for the convergence', xaxis_title='tau', yaxis_title='time (seconds)'))
+
+        # save the plot in a html file
+        fig.write_html("../data/results/algo1/taus_over_time.html")
+        print("The plot has been saved in the folder data/results/algo1")
+
+class Algorithms:
+    def algo1(Pt, v, tau, max_mv, a: list):
+        start_time = time.time()
+
+        print("STARTING ALGORITHM 1...")
+        u = Pt.dot(v) - v
+        mv = 1 # number of iteration
+        r = sp.sparse.lil_matrix((n,1))
+        Res = sp.sparse.lil_matrix((len(a),1))
+        x = sp.sparse.lil_matrix((n,1))
+
+        for i in range(len(a)):
+            r = a[i]*(u)
+            normed_r = norm(r)
+            Res[i] = normed_r
+
+            if Res[i] > tau:
+                x = r + v
+
+        while max(Res) > tau and mv < max_mv:
+            u = Pt*u # should it be the same u of the beginning?
+            mv += 1
+
+            for i in range(len(a)):
+                if Res[i] >= tau:
+                    r = (a[i]**(mv+1))*(u)
+                    Res[i] = norm(r)
+
+                    if Res[i] > tau:
+                        x = r + x
+
+        if mv == max_mv:
+            print("The algorithm didn't converge in ", max_mv, " iterations")
+        else:
+            print("The algorithm converged in ", mv, " iterations")
+
+        total_time = time.time() - start_time
+        total_time = round(total_time, 2)
+
+        print("The algorithm took ", total_time, " seconds to run\n")
+
+        return mv, x, r, total_time
+
+# pandas dataframe to store the results
+df = pd.DataFrame(columns=['alpha', 'iterations', 'tau', 'time'])
+
+# Main
+if __name__ == "__main__":
+    dataset = utilities.load_data()
+    # maximum number of iterations, asked to the user
+    max_mv = int(input("Insert the maximum number of iterations: "))
+
+    G, n = utilities.create_graph(dataset)
+    P = utilities.create_matrix(G)
+    d = utilities.dangling_nodes(P,n)
+    v = utilities.probability_vector(n)
+    Pt = utilities.transition_matrix(P, v, d)
+    a = utilities.alpha()
+
+    # run the algorithm for different values of tau from 10^-5 to 10^-9 with step 10^-1
+    for i in range(5,10):
+        tau = 10**(-i)
+        print("\ntau = ", tau)
+        mv, x, r, total_time = Algorithms.algo1(Pt, v, tau, max_mv, a)
+
+        # store the results in the dataframe
+        df = df.append({'alpha': a, 'iterations': mv, 'tau': tau, 'time': total_time}, ignore_index=True)
+
+    # save the results in a csv file
+    df.to_csv('../data/results/algo1/different_tau.csv', index=False)
+
+    # plot the results
+    Plotting.tau_over_iterations(df)
+    Plotting.tau_over_time(df)
+
+    # print in the terminal the columns of the dataframe iterations, tau and time
+    print("\n", df[['iterations', 'tau', 'time']])