mp2: done 1-6
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6 changed files with 133 additions and 26 deletions
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@ -3,6 +3,11 @@ clc;
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load('householder/housegraph.mat')
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load('householder/housegraph.mat')
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names = split(strtrim(convertCharsToStrings(name')));
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names = split(strtrim(convertCharsToStrings(name')));
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common1 = names((A(:,Golub) .* A(:, Moler)) == 1)
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disp("Golub-Moler:");
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common2 = names((A(:,Golub) .* A(:, Saunders)) == 1)
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disp(names((A(:,Golub) .* A(:, Moler)) == 1));
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common3 = names((A(:,TChan) .* A(:, Demmel)) == 1)
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disp("Golub-Saunders:");
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disp(names((A(:,Golub) .* A(:, Saunders)) == 1));
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disp("TChan-Demmel:");
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disp(names((A(:,TChan) .* A(:, Demmel)) == 1));
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6
mp2/Project.2.Maggioni.Claudio/ex5.m
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6
mp2/Project.2.Maggioni.Claudio/ex5.m
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@ -0,0 +1,6 @@
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clear;
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clc;
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load('householder/housegraph.mat')
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names = split(strtrim(convertCharsToStrings(name')));
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pagerank(names, A);
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@ -8,43 +8,31 @@ function x = pagerank(U,G,p)
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if nargin < 3, p = .85; end
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if nargin < 3, p = .85; end
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if(ischar(U))
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U=cellstr(U);
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end
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if(isreal(U))
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U=(num2cell(U));
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end
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% Eliminate any self-referential links
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% Eliminate any self-referential links
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%G = G - diag(diag(G));
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G = G - diag(diag(G));
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% c = out-degree, r = in-degree
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% c = out-degree, r = in-degree
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[~,n] = size(G);
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n = size(G,1);
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c = sum(G,1);
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c = sum(G,1);
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r = sum(G,2);
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r = sum(G,2);
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% Scale column sums to be 1 (or 0 where there are no out links).
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% Scale column sums to be 1 (or 0 where there are no out links).
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k = find(c~=0);
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k = find(c~=0);
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D = sparse(k,k,1./c(k),n,n);
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D = sparse(k,k,1./c(k),n,n);
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% Solve (I - p*G*D)*x = e
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e = ones(n,1);
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e = ones(n,1);
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I = speye(n,n);
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I = speye(n,n);
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% ---------------------------------- DEFAULT ------------------------------
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% Solve (I - p*G*D)*x = e
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x = (I - p*G*D)\e;
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x = (I - p*G*D)\e;
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% Normalize so that sum(x) == 1.
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% -------------------------------------------------------------------------
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% Normalize so that sum(x) == 1.
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x = x/sum(x);
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x = x/sum(x);
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% Bar graph of page rank.
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% Bar graph of page rank.
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shg
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shg
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bar(x)
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bar(x)
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title('Page Rank')
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title('Page Rank')
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@ -53,13 +41,14 @@ title('Page Rank')
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if nargout < 1
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if nargout < 1
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[~,q] = sort(-x);
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[~,q] = sort(-x);
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disp(' page-rank in out url')
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disp(' page-rank in out author');
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k = 1;
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k = 1;
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while (k <= n) && (x(q(k)) >= .005)
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maxN = length(U);
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while (k <= maxN) && (x(q(k)) >= .005)
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j = q(k);
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j = q(k);
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temp1 = r(j);
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temp1 = r(j);
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temp2 = c(j);
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temp2 = c(j);
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fprintf(' %3.0f %8.4f %4.0f %4.0f %s\n', j,x(j),full(temp1),full(temp2),U{j})
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fprintf(' %3.0f %8.4f %4.0f %4.0f %s\n', j,x(j),full(temp1),full(temp2),U{j});
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k = k+1;
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k = k+1;
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end
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end
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end
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end
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Binary file not shown.
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@ -118,7 +118,7 @@ Assuming that the degree of the Householder graph is the number of co-authors of
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each author and that an author is not co-author of himself, the degree
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each author and that an author is not co-author of himself, the degree
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centralities of all authors sorted in descending order are below.
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centralities of all authors sorted in descending order are below.
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This output has been obtained by running \texttt{ex2.m}.
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This output has been obtained by running \texttt{ex3.m}.
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\begin{verbatim}
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\begin{verbatim}
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Author Centrality: Coauthors...
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Author Centrality: Coauthors...
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@ -248,6 +248,8 @@ as:
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\[C = \{i \in N_0 \;|\; (A_{:,i} \odot A_{:,j})_i = 1\}\]
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\[C = \{i \in N_0 \;|\; (A_{:,i} \odot A_{:,j})_i = 1\}\]
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The results below were computing by using the script \texttt{ex4.m}.
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The common Co-authors between Golub and Moler are Wilkinson and Van Loan.
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The common Co-authors between Golub and Moler are Wilkinson and Van Loan.
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The common Co-authors between Golub and Saunders are Golub, Saunders and Gill.
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The common Co-authors between Golub and Saunders are Golub, Saunders and Gill.
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@ -257,6 +259,111 @@ Heath.
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\section{PageRank of the Coauthor Graph [10 points]}
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\section{PageRank of the Coauthor Graph [10 points]}
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The PageRank values for all authors were computing by using the scripts
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\texttt{ex5.m} and \texttt{pagerank.m}, a basically identical version of
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\texttt{pagerank.m} from Mini Project 1. The output is shown below.
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\begin{verbatim}
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page-rank in out author
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1 0.0511 32 32 Golub
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104 0.0261 16 16 Demmel
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86 0.0229 14 14 Plemmons
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44 0.0212 13 13 Schreiber
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3 0.0201 11 11 TChan
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81 0.0198 13 13 Heath
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90 0.0181 10 10 Gragg
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74 0.0177 11 11 Hammarling
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66 0.0171 11 11 VanDooren
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42 0.0152 9 9 Moler
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79 0.0151 8 8 Gutknecht
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32 0.0142 9 9 VanLoan
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59 0.0135 8 8 Eisenstat
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98 0.0133 8 8 Paige
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46 0.0130 7 7 NTrefethen
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49 0.0129 6 6 Varga
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96 0.0128 7 7 Meyer
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77 0.0128 7 7 Stewart
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73 0.0127 8 8 Luk
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78 0.0127 7 7 Bunch
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53 0.0127 6 6 Widlund
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72 0.0125 7 7 Reichel
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41 0.0125 8 8 George
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82 0.0124 6 6 Ipsen
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83 0.0122 6 6 Greenbaum
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58 0.0113 7 7 Bjorck
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97 0.0107 6 6 Nichols
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51 0.0106 6 6 Kagstrom
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80 0.0106 6 6 Laub
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52 0.0104 6 6 Barlow
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60 0.0103 6 6 Zha
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69 0.0102 6 6 Duff
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62 0.0100 6 6 Park
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89 0.0099 5 5 BunseGerstner
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63 0.0098 5 5 Arioli
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43 0.0097 6 6 Gilbert
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67 0.0096 6 6 Liu
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87 0.0096 5 5 Hansen
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47 0.0090 5 5 Nachtigal
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54 0.0090 4 4 Bjorstad
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2 0.0088 5 5 Wilkinson
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23 0.0088 5 5 Harrod
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99 0.0087 5 5 Gill
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92 0.0086 5 5 Sameh
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91 0.0086 5 5 Berry
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15 0.0086 5 5 Boley
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76 0.0085 4 4 Fischer
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50 0.0085 3 3 Young
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61 0.0084 5 5 VanHuffel
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100 0.0084 3 3 Jessup
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48 0.0083 4 4 Kahan
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35 0.0083 5 5 Bojanczyk
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65 0.0082 5 5 Ng
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93 0.0082 4 4 Ammar
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55 0.0079 4 4 OLeary
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84 0.0079 3 3 Ruhe
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19 0.0078 4 4 Kaufman
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56 0.0076 4 4 NHigham
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37 0.0075 3 3 Marek
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75 0.0075 3 3 Szyld
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103 0.0074 3 3 Starke
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34 0.0072 4 4 Saunders
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25 0.0072 4 4 Funderlic
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39 0.0072 4 4 Bai
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102 0.0072 3 3 Hochbruck
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88 0.0071 4 4 Elden
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71 0.0070 4 4 Tang
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38 0.0069 3 3 Kuo
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40 0.0069 3 3 Tong
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4 0.0068 3 3 He
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13 0.0067 2 2 Kincaid
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14 0.0067 2 2 Crevelli
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94 0.0065 3 3 Warner
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17 0.0065 3 3 Byers
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21 0.0064 3 3 Fierro
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31 0.0064 2 2 Wold
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45 0.0062 3 3 Pothen
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36 0.0060 3 3 Dubrulle
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57 0.0058 2 2 Boman
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10 0.0058 3 3 Overton
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9 0.0057 2 2 Modersitzki
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68 0.0056 2 2 Smith
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95 0.0056 2 2 Davis
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33 0.0056 2 2 Chandrasekaran
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27 0.0055 2 2 Cullum
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28 0.0055 2 2 Strakos
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64 0.0054 2 2 MuntheKaas
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7 0.0053 2 2 Ashby
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85 0.0053 2 2 ATrefethen
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29 0.0052 2 2 Saied
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30 0.0052 2 2 Ong
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18 0.0052 2 2 Benzi
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101 0.0052 2 2 Mathias
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8 0.0052 2 2 LeBorne
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12 0.0052 2 2 Borges
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6 0.0051 2 2 Kenney
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70 0.0050 2 2 Henrici
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\end{verbatim}
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\section{Zachary's karate club: social network of friendships between 34 members [50 points]}
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\section{Zachary's karate club: social network of friendships between 34 members [50 points]}
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\begin{thebibliography}{99}
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\begin{thebibliography}{99}
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