From f94cef9935f749a1236f29d3d208706a339e0968 Mon Sep 17 00:00:00 2001 From: Luca Lombardo Date: Tue, 26 Apr 2022 16:31:13 +0200 Subject: [PATCH] tyos and merged with upstream --- .../actor_bench/closeness_results/analysis.py | 4 +++- tex/src/abstract.tex | 2 +- tex/src/main.pdf | Bin 2043063 -> 2021930 bytes 3 files changed, 4 insertions(+), 2 deletions(-) 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. 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