diff --git a/scripts/actor_bench/closeness_results/analysis.py b/scripts/actor_bench/closeness_results/analysis.py
index 6382966..ccc5108 100755
--- a/scripts/actor_bench/closeness_results/analysis.py
+++ b/scripts/actor_bench/closeness_results/analysis.py
@@ -3,7 +3,7 @@ import os
 import matplotlib.pyplot as plt
 import numpy as np
 import pandas as pd
-
+# %%
 dfs = {
     i: pd.read_csv(f"top_actors_{i:02d}_c.txt", sep='\t', usecols=[1], names=["actor"])
     for i in [5] + list(range(10, 71, 10))}
@@ -27,3 +27,5 @@ plt.xlabel("\nMIN_ACTORS value")
 cb = plt.colorbar()
 cb.set_label("\npercentace of difference in results varing MIN_MOVIES")
 plt.show()
+
+# %% 3 + 3
diff --git a/tex/src/abstract.tex b/tex/src/abstract.tex
index 7595c15..f1dfd79 100644
--- a/tex/src/abstract.tex
+++ b/tex/src/abstract.tex
@@ -1,4 +1,4 @@
-Understanding and investigating social structures is essential in the modern world. Through the use of networks and graph theory we can find the most central elements in a community. In particolar, given a connected graph $G=(V,E)$, the closeness centrality of a vertex $v$ is defined as $ \frac{n-1}{\sum_{w \in V} d(v,w)}$. This measure can be seen as the efficiency of a node to pass information through all the other nodes in the graph. In this paper we will discuss an algorithm and its result in finding the top-k most central elements in web-scale graphs. As a case study, we are going to use the IMDB collaboration network, building two completely different graphs and analyzing their proprieties.
+Understanding and investigating social structures is essential in the modern world. Through the use of networks and graph theory we can find the most central elements in a community. In particoular, given a connected graph $G=(V,E)$, the closeness centrality of a vertex $v$ is defined as $ \frac{n-1}{\sum_{w \in V} d(v,w)}$. This measure can be seen as the efficiency of a node to pass information through all the other nodes in the graph. In this paper we will discuss an algorithm and its results for finding the $k$ most central elements in web-scale graphs. As a case study, we are going to use the IMDB collaboration network, building two completely different graphs and analyzing their proprieties.
 
 % Given a connected graph $G=(V,E)$, the closeness centrality of a vertex $v$ is defined as $ \frac{n-1}{\sum_{w \in V} d(v,w)}$. This measure is widely used in the analysis of real-world complex networks, and the problem of selecting the $k$ most central vertices has been deeply analysed in the last decade. However, this problem is computationally not easy, especially for large networks. I propose an algorithm for selecting the $k$ most central nodes in a graph: I experimentally show that this algorithm improves significantly both the textbook algorithm, which is based on computing the distance between all pairs of vertices, and the state of the art. Finally, as a case study, I compute the $10$ most central actors in the IMDB collaboration network, where two actors are linked if they played together in a movie.
 
diff --git a/tex/src/main.pdf b/tex/src/main.pdf
index 8b05678..09c0a55 100644
Binary files a/tex/src/main.pdf and b/tex/src/main.pdf differ