From 58f77aad4ab7fbc907d7080238a6872bd3260724 Mon Sep 17 00:00:00 2001 From: noah Date: Tue, 25 Apr 2023 18:52:38 -0500 Subject: [PATCH] Incorporating edits --- Schrick-Noah_CG-Network_Theory.aux | 32 +-- Schrick-Noah_CG-Network_Theory.log | 116 +++++---- Schrick-Noah_CG-Network_Theory.pdf | Bin 200465 -> 411022 bytes Schrick-Noah_CG-Network_Theory.tex | 165 +++---------- Schrick-Noah_Supplemental.aux | 53 +++-- Schrick-Noah_Supplemental.log | 361 ++++++++++++++++------------- Schrick-Noah_Supplemental.pdf | Bin 53763 -> 60572 bytes Schrick-Noah_Supplemental.tex | 143 ++++++++++++ images/car-betweenness.png | Bin 101737 -> 77731 bytes images/car-degree.png | Bin 81399 -> 82854 bytes images/car-katz.png | Bin 93919 -> 74379 bytes images/car-kpe.png | Bin 89704 -> 77661 bytes images/car-pagerank.png | Bin 114047 -> 70968 bytes 13 files changed, 476 insertions(+), 394 deletions(-) diff --git a/Schrick-Noah_CG-Network_Theory.aux b/Schrick-Noah_CG-Network_Theory.aux index 5707255..d6cdf28 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a/Schrick-Noah_Supplemental.tex +++ b/Schrick-Noah_Supplemental.tex @@ -40,10 +40,153 @@ Tulsa, USA \\ peter-hawrylak@utulsa.edu } + + \and + + \IEEEauthorblockN{Brett A. McKinney} + \IEEEauthorblockA{ + \textit{Tandy School of Computer Science} \\ + \textit{The University of Tulsa}\\ + Tulsa, USA \\ + brett-mckinney@utulsa.edu + } } \maketitle +\begin{table}[] + \centering + \setlength\tabcolsep{4pt} + \begin{tabular}{|cc|cc|cc|} + \hline + + \multicolumn{2}{|c|}{\textbf{Base}} + & \multicolumn{2}{|c|}{\textbf{Transitive Closure}} + & \multicolumn{2}{|c|}{\textbf{Dominant Tree}} + \\ \hline + + \multicolumn{1}{|c|}{\textbf{Node}} & \textbf{\% Value} & \multicolumn{1}{c|}{\textbf{Node}} & \textbf{\% Value} & \multicolumn{1}{c|}{\textbf{Node}} & \textbf{\% Value} \\ \hline + \multicolumn{1}{|c|}{314} & 0.13 & \multicolumn{1}{c|}{0} & 9.09 & \multicolumn{1}{c|}{1} & 4.88 \\ \hline + \multicolumn{1}{|c|}{377} & 0.10 & \multicolumn{1}{c|}{1} & 8.26 & \multicolumn{1}{c|}{3} & 3.47 \\ \hline + \multicolumn{1}{|c|}{346} & 0.10 & \multicolumn{1}{c|}{3} & 7.39 & \multicolumn{1}{c|}{7} & 0.60 \\ \hline + \multicolumn{1}{|c|}{376} & 0.10 & \multicolumn{1}{c|}{7} & 6.34 & \multicolumn{1}{c|}{0} & 0.52 \\ \hline + \multicolumn{1}{|c|}{374} & 0.10 & \multicolumn{1}{c|}{15} & 5.27 & \multicolumn{1}{c|}{42} & 0.45 \\ \hline + \multicolumn{1}{|c|}{378} & 0.10 & \multicolumn{1}{c|}{27} & 4.37 & \multicolumn{1}{c|}{314} & 0.15 \\ \hline + \multicolumn{1}{|c|}{380} & 0.10 & \multicolumn{1}{c|}{42} & 3.61 & \multicolumn{1}{c|}{27} & 0.08 \\ \hline + \multicolumn{1}{|c|}{381} & 0.10 & \multicolumn{1}{c|}{60} & 2.71 & \multicolumn{1}{c|}{250} & 0.05 \\ \hline + \multicolumn{1}{|c|}{382} & 0.10 & \multicolumn{1}{c|}{87} & 2.02 & \multicolumn{1}{c|}{15} & 0.04 \\ \hline + \multicolumn{1}{|c|}{262} & 0.10 & \multicolumn{1}{c|}{130} & 1.48 & \multicolumn{1}{c|}{187} & 0.04 \\ \hline + \multicolumn{1}{|c|}{370} & 0.10 & \multicolumn{1}{c|}{2} & 1.31 & \multicolumn{1}{c|}{130} & 0.04 \\ \hline + \multicolumn{1}{|c|}{379} & 0.10 & \multicolumn{1}{c|}{4} & 1.19 & \multicolumn{1}{c|}{87} & 0.04 \\ \hline + \multicolumn{1}{|c|}{418} & 0.08 & \multicolumn{1}{c|}{5} & 1.19 & \multicolumn{1}{c|}{60} & 0.04 \\ \hline + \multicolumn{1}{|c|}{459} & 0.08 & \multicolumn{1}{c|}{6} & 1.19 & \multicolumn{1}{c|}{2} & 0.04 \\ \hline + \multicolumn{1}{|c|}{467} & 0.08 & \multicolumn{1}{c|}{187} & 1.08 & \multicolumn{1}{c|}{4} & 0.04 \\ \hline + + \end{tabular} + \caption{Top 15 Nodes with Katz Centrality for the Automobile Network. \\\hspace{\textwidth} Base columns represent the top ranked nodes and their percentage of importance held relative to the entire network. \\\hspace{\textwidth}Transitive Closure and Dominant Tree columns illustrate the difference in node rankings after the base network underwent a transformation. \\\hspace{\textwidth}} + \label{table:car-katz} +\end{table} + +\begin{table}[] + \centering + \setlength\tabcolsep{4pt} + \begin{tabular}{|cc|cc|cc|} + \hline + + \multicolumn{2}{|c|}{\textbf{Base}} + & \multicolumn{2}{|c|}{\textbf{Transitive Closure}} + & \multicolumn{2}{|c|}{\textbf{Dominant Tree}} + \\ \hline + + \multicolumn{1}{|c|}{\textbf{Node}} & \textbf{\% Value} & \multicolumn{1}{c|}{\textbf{Node}} & \textbf{\% Value} & \multicolumn{1}{c|}{\textbf{Node}} & \textbf{\% Value} \\ \hline + \multicolumn{1}{|c|}{314} & 0.25 & \multicolumn{1}{c|}{0} & 0.65 & \multicolumn{1}{c|}{1} & 37.54 \\ \hline + \multicolumn{1}{|c|}{346} & 0.19 & \multicolumn{1}{c|}{1} & 0.39 & \multicolumn{1}{c|}{0} & 35.05 \\ \hline + \multicolumn{1}{|c|}{362} & 0.19 & \multicolumn{1}{c|}{3} & 0.65 & \multicolumn{1}{c|}{3} & 17.53 \\ \hline + \multicolumn{1}{|c|}{370} & 0.19 & \multicolumn{1}{c|}{7} & 0.65 & \multicolumn{1}{c|}{7} & 2.54 \\ \hline + \multicolumn{1}{|c|}{374} & 0.19 & \multicolumn{1}{c|}{15} & 0.64 & \multicolumn{1}{c|}{15} & 1.88 \\ \hline + \multicolumn{1}{|c|}{376} & 0.19 & \multicolumn{1}{c|}{27} & 0.64 & \multicolumn{1}{c|}{27} & 1.88 \\ \hline + \multicolumn{1}{|c|}{377} & 0.19 & \multicolumn{1}{c|}{42} & 0.64 & \multicolumn{1}{c|}{42} & 1.88 \\ \hline + \multicolumn{1}{|c|}{378} & 0.19 & \multicolumn{1}{c|}{60} & 0.62 & \multicolumn{1}{c|}{187} & 0.53 \\ \hline + \multicolumn{1}{|c|}{379} & 0.19 & \multicolumn{1}{c|}{87} & 0.60 & \multicolumn{1}{c|}{250} & 0.51 \\ \hline + \multicolumn{1}{|c|}{380} & 0.19 & \multicolumn{1}{c|}{130} & 0.59 & \multicolumn{1}{c|}{314} & 0.50 \\ \hline + \multicolumn{1}{|c|}{381} & 0.19 & \multicolumn{1}{c|}{187} & 0.57 & \multicolumn{1}{c|}{60} & 0.05 \\ \hline + \multicolumn{1}{|c|}{382} & 0.19 & \multicolumn{1}{c|}{250} & 0.55 & \multicolumn{1}{c|}{86} & 0.05 \\ \hline + \multicolumn{1}{|c|}{398} & 0.14 & \multicolumn{1}{c|}{314} & 0.54 & \multicolumn{1}{c|}{130} & 0.05 \\ \hline + \multicolumn{1}{|c|}{406} & 0.14 & \multicolumn{1}{c|}{2} & 0.33 & \multicolumn{1}{c|}{2} & 0.00 \\ \hline + \multicolumn{1}{|c|}{410} & 0.14 & \multicolumn{1}{c|}{4} & 0.33 & \multicolumn{1}{c|}{4} & 0.00 \\ \hline + + \end{tabular} + \caption{Top 15 Nodes with K-path Edge Centrality for the Automobile Network. \\\hspace{\textwidth} Base columns represent the top ranked nodes and their percentage of importance held relative to the entire network. \\\hspace{\textwidth}Transitive Closure and Dominant Tree columns illustrate the difference in node rankings after the base network underwent a transformation. \\\hspace{\textwidth}} + \label{table:car-kpe} +\end{table} + +\begin{table}[] + \centering + \setlength\tabcolsep{4pt} + \begin{tabular}{|cc|cc|cc|} + \hline + + \multicolumn{2}{|c|}{\textbf{Base}} + & \multicolumn{2}{|c|}{\textbf{Transitive Closure}} + & \multicolumn{2}{|c|}{\textbf{Dominant Tree}} + \\ \hline + + \multicolumn{1}{|c|}{\textbf{Node}} & \textbf{\% Value} & \multicolumn{1}{c|}{\textbf{Node}} & \textbf{\% Value} & \multicolumn{1}{c|}{\textbf{Node}} & \textbf{\% Value} \\ \hline + \multicolumn{1}{|c|}{2490} & 8.27 & \multicolumn{1}{c|}{2490} & 19.92 & \multicolumn{1}{c|}{314} & 0.17 \\ \hline + \multicolumn{1}{|c|}{1004} & 1.06 & \multicolumn{1}{c|}{2479} & 1.58 & \multicolumn{1}{c|}{250} & 0.15 \\ \hline + \multicolumn{1}{|c|}{1467} & 0.97 & \multicolumn{1}{c|}{2480} & 1.58 & \multicolumn{1}{c|}{187} & 0.13 \\ \hline + \multicolumn{1}{|c|}{2479} & 0.95 & \multicolumn{1}{c|}{2481} & 1.58 & \multicolumn{1}{c|}{130} & 0.10 \\ \hline + \multicolumn{1}{|c|}{2480} & 0.95 & \multicolumn{1}{c|}{2482} & 1.58 & \multicolumn{1}{c|}{42} & 0.10 \\ \hline + \multicolumn{1}{|c|}{2481} & 0.95 & \multicolumn{1}{c|}{2483} & 1.58 & \multicolumn{1}{c|}{87} & 0.07 \\ \hline + \multicolumn{1}{|c|}{2482} & 0.95 & \multicolumn{1}{c|}{2484} & 1.4 & \multicolumn{1}{c|}{27} & 0.07 \\ \hline + \multicolumn{1}{|c|}{2483} & 0.95 & \multicolumn{1}{c|}{2485} & 1.4 & \multicolumn{1}{c|}{1} & 0.07 \\ \hline + \multicolumn{1}{|c|}{667} & 0.92 & \multicolumn{1}{c|}{2486} & 1.39 & \multicolumn{1}{c|}{378} & 0.04 \\ \hline + \multicolumn{1}{|c|}{2484} & 0.83 & \multicolumn{1}{c|}{2487} & 1.39 & \multicolumn{1}{c|}{379} & 0.04 \\ \hline + \multicolumn{1}{|c|}{2485} & 0.83 & \multicolumn{1}{c|}{2488} & 1.39 & \multicolumn{1}{c|}{380} & 0.04 \\ \hline + \multicolumn{1}{|c|}{2486} & 0.83 & \multicolumn{1}{c|}{2489} & 1.39 & \multicolumn{1}{c|}{381} & 0.04 \\ \hline + \multicolumn{1}{|c|}{2487} & 0.83 & \multicolumn{1}{c|}{2424} & 0.29 & \multicolumn{1}{c|}{382} & 0.04 \\ \hline + \multicolumn{1}{|c|}{2488} & 0.83 & \multicolumn{1}{c|}{2425} & 0.29 & \multicolumn{1}{c|}{470} & 0.04 \\ \hline + \multicolumn{1}{|c|}{2489} & 0.83 & \multicolumn{1}{c|}{2426} & 0.29 & \multicolumn{1}{c|}{471} & 0.04 \\ \hline + + \end{tabular} + \caption{Top 15 Nodes with PageRank Centrality for the Automobile Network. \\\hspace{\textwidth} Base columns represent the top ranked nodes and their percentage of importance held relative to the entire network. \\\hspace{\textwidth}Transitive Closure and Dominant Tree columns illustrate the difference in node rankings after the base network underwent a transformation. \\\hspace{\textwidth}} + \label{table:car-APC} +\end{table} + +\begin{table}[] + \centering + \setlength\tabcolsep{4pt} + \begin{tabular}{|cc|cc|cc|} + \hline + + \multicolumn{2}{|c|}{\textbf{Base}} + & \multicolumn{2}{|c|}{\textbf{Transitive Closure}} + & \multicolumn{2}{|c|}{\textbf{Dominant Tree}} + \\ \hline + + \multicolumn{1}{|c|}{\textbf{Node}} & \textbf{\% Value} & \multicolumn{1}{c|}{\textbf{Node}} & \textbf{\% Value} & \multicolumn{1}{c|}{\textbf{Node}} & \textbf{\% Value} \\ \hline + \multicolumn{1}{|c|}{42} & 0.43 & \multicolumn{1}{c|}{0} & 0 & \multicolumn{1}{c|}{1} & 24.71 \\ \hline + \multicolumn{1}{|c|}{27} & 0.40 & \multicolumn{1}{c|}{1} & 0 & \multicolumn{1}{c|}{3} & 24.68 \\ \hline + \multicolumn{1}{|c|}{60} & 0.39 & \multicolumn{1}{c|}{2} & 0 & \multicolumn{1}{c|}{7} & 9.20 \\ \hline + \multicolumn{1}{|c|}{87} & 0.36 & \multicolumn{1}{c|}{3} & 0 & \multicolumn{1}{c|}{42} & 9.00 \\ \hline + \multicolumn{1}{|c|}{15} & 0.36 & \multicolumn{1}{c|}{4} & 0 & \multicolumn{1}{c|}{27} & 7.55 \\ \hline + \multicolumn{1}{|c|}{130} & 0.33 & \multicolumn{1}{c|}{5} & 0 & \multicolumn{1}{c|}{15} & 6.08 \\ \hline + \multicolumn{1}{|c|}{7} & 0.31 & \multicolumn{1}{c|}{6} & 0 & \multicolumn{1}{c|}{314} & 3.69 \\ \hline + \multicolumn{1}{|c|}{187} & 0.29 & \multicolumn{1}{c|}{7} & 0 & \multicolumn{1}{c|}{250} & 3.49 \\ \hline + \multicolumn{1}{|c|}{50} & 0.28 & \multicolumn{1}{c|}{8} & 0 & \multicolumn{1}{c|}{187} & 3.28 \\ \hline + \multicolumn{1}{|c|}{70} & 0.28 & \multicolumn{1}{c|}{9} & 0 & \multicolumn{1}{c|}{130} & 3.04 \\ \hline + \multicolumn{1}{|c|}{104} & 0.27 & \multicolumn{1}{c|}{10} & 0 & \multicolumn{1}{c|}{87} & 2.78 \\ \hline + \multicolumn{1}{|c|}{156} & 0.26 & \multicolumn{1}{c|}{11} & 0 & \multicolumn{1}{c|}{60} & 2.50 \\ \hline + \multicolumn{1}{|c|}{1467} & 0.25 & \multicolumn{1}{c|}{12} & 0 & \multicolumn{1}{c|}{0} & 0.00 \\ \hline + \multicolumn{1}{|c|}{250} & 0.25 & \multicolumn{1}{c|}{13} & 0 & \multicolumn{1}{c|}{2} & 0.00 \\ \hline + \multicolumn{1}{|c|}{115} & 0.25 & \multicolumn{1}{c|}{14} & 0 & \multicolumn{1}{c|}{4} & 0.00 \\ \hline + + \end{tabular} + \caption{Top 15 Nodes with Betweenness Centrality for the Automobile Network. \\\hspace{\textwidth} Base columns represent the top ranked nodes and their percentage of importance held relative to the entire network. \\\hspace{\textwidth}Transitive Closure and Dominant Tree columns illustrate the difference in node rankings after the base network underwent a transformation. \\\hspace{\textwidth}} + \label{table:car-betweenness} +\end{table} + + \begin{table}[] \centering \setlength\tabcolsep{4pt} diff --git a/images/car-betweenness.png b/images/car-betweenness.png index 1f817d1180294f6ac1ff720555c7cae1a819dc68..7aa3c1dc31ef3f8a43b6f799d5c1915c1a082186 100644 GIT binary patch literal 77731 zcmeFYRaBfow>F40ZjF0r5+FFiEl8umHMm29yE|!uBsf8Wy9IZ54el-hg1bA+n{&>$ z=AT*r#jG`J?xt_L>+S05l5Mr0XMa;xl*U3QLx+Qd!;<+Rp$Z3w2!(?~7(+z{p5(q8 z>IL55omHj9;L1iR_J9V+SxiP96?plenuWr_LEvO0pz0n5hiNE2YBR+BIB^OX1IW1A z2-v}hV5r1X@qpBV_em=+>cA@b;HnxJ_bs+Et~yx7?DwiSku1jJ*hw7mWOR*83K!e& 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