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Formatting first two tables in tex

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Noah L. Schrick 2022-10-11 15:02:54 -05:00
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6 changed files with 777 additions and 425 deletions
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\BOOKMARK [1][-]{section*.11}{\376\377\000A\000p\000p\000e\000n\000d\000i\000x}{}% 26

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@ -1,5 +1,5 @@
\documentclass[conference]{IEEEtran}
\RequirePackage{setspace}
\documentclass{article}
\usepackage{boxedminipage}
\usepackage{graphicx} % Images
\graphicspath{ {./images/} }
@ -29,14 +29,40 @@
\cftsetindents{figure}{0em}{3.5em}
\cftsetindents{table}{0em}{3.5em}
\title{CS 7863: Network Theory Final Project: Compliance Graph Analysis}
\author{Noah Schrick}
\date{May 3, 2022}
\begin{document}
\title{
Placeholder Title
}
\author{
\IEEEauthorblockN{Noah L. Schrick}
\IEEEauthorblockA{
\textit{Tandy School of Computer Science} \\
\textit{The University of Tulsa}\\
Tulsa, USA \\
noah-schrick@utulsa.edu
}
\and
\IEEEauthorblockN{Peter J. Hawrylak}
\IEEEauthorblockA{
\textit{Tandy School of Computer Science} \\
\textit{The University of Tulsa}\\
Tulsa, USA \\
peter-hawrylak@utulsa.edu
}
}
\maketitle
\tableofcontents
\begin{abstract}
\end{abstract}
\begin{IEEEkeywords}
Attack Graph; Compliance Graph; Cybersecurity; Compliance and Regulation; Network Theory; Centrality;
\end{IEEEkeywords}
\section{Introduction}
\subsection{Attack Graphs}
@ -49,7 +75,7 @@ Compliance graphs are an alternate form of attack graphs, utilized specifically
The semantics of compliance graphs are similar to that of attack graphs, but with a few differences regarding the information at each state. While security and compliance statuses are related, the information that is analyzed in compliance graphs is focused less on certain security properties, and is expanded to also examine administrative policies and properties of systems. Since compliance and regulation is broad and can vary by industry and application, the information to analyze can range from safety regulations, maintenance compliance, or any other regulatory compliance. However, the graph structure of compliance graphs is identical to that of attack graphs, where edges represent a modification to the systems, and nodes represent all current information in the system.
\subsection{Difficulties of Compliance Graph Analysis}
\subsection{Difficulties of Attack and Compliance Graph Analysis}
Analysis of directed graphs is not as simple as their undirected counterparts, and attack and compliance graphs are directed acyclic graphs. The primary contributor to the increased difficulty is due to the asymmetric adjacency matrix present in directed graphs. With undirected graphs, simplifications can be made in the analysis process both computationally and conceptually. Since the ``in" degrees are equal to the ``out" degrees, less work is required both in terms of parsing the adjacency matrix, but also in terms of determining importance of nodes. The author of \cite{newman2010networks} discusses that common analysis techniques such as eigenvector centrality is often unapplicable to directed acyclic graphs. As the author of \cite{Mieghem2018DirectedGA} discusses, the difficulty of directed graphs also extends to the graph Laplacian, where the definition for asymmetric adjacency matrices is not uniquely defined, and is based on either row or column sums computing to zero, but both cannot. The author of \cite{Mieghem2018DirectedGA} continues to discuss that directed graphs lead to complex eigenvalues, and can lead to adjacency matrices that are unable to be diagonalized. These challenges require different approaches for typical clustering or centrality measures.
\section{Related Works}
@ -175,23 +201,93 @@ In this section, only results for the car network are displayed for brevity. The
\centering
\begin{tabular}{|cc|cc|cc|}
\hline
\multicolumn{2}{|c|}{\cellcolor[HTML]{FFFF00}\textbf{Base}} & \multicolumn{2}{|c|}{\cellcolor[HTML]{FFFF00}\textbf{Transitive Closure}} & \multicolumn{2}{|c|}{\cellcolor[HTML]{FFFF00}\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} & 11 & \multicolumn{1}{|c|}{0} & \multicolumn{1}{|c|}{2490} & \multicolumn{1}{|c|}{1} & \multicolumn{1}{|c|}{1246} \\ \hline
\multicolumn{1}{|c|}{346} & 10 & \multicolumn{1}{|c|}{1} & \multicolumn{1}{|c|}{2489} & \multicolumn{1}{|c|}{3} & \multicolumn{1}{|c|}{934} \\ \hline
\multicolumn{1}{|c|}{362} & 10 & \multicolumn{1}{|c|}{3} & \multicolumn{1}{|c|}{2487} & \multicolumn{1}{|c|}{7} & \multicolumn{1}{|c|}{156} \\ \hline
\multicolumn{1}{|c|}{370} & 10 & \multicolumn{1}{|c|}{7} & \multicolumn{1}{|c|}{2479} & \multicolumn{1}{|c|}{42} & \multicolumn{1}{|c|}{115} \\ \hline
\multicolumn{1}{|c|}{374} & 10 & \multicolumn{1}{|c|}{15} & \multicolumn{1}{|c|}{2463} & \multicolumn{1}{|c|}{314} & \multicolumn{1}{|c|}{31} \\ \hline
\multicolumn{1}{|c|}{376} & 10 & \multicolumn{1}{|c|}{27} & \multicolumn{1}{|c|}{2447} & \multicolumn{1}{|c|}{0} & \multicolumn{1}{|c|}{1} \\ \hline
\multicolumn{1}{|c|}{377} & 10 & \multicolumn{1}{|c|}{42} & \multicolumn{1}{|c|}{2431} & \multicolumn{1}{|c|}{15} & \multicolumn{1}{|c|}{1} \\ \hline
\multicolumn{1}{|c|}{378} & 10 & \multicolumn{1}{|c|}{60} & \multicolumn{1}{|c|}{2367} & \multicolumn{1}{|c|}{27} & \multicolumn{1}{|c|}{1} \\ \hline
\multicolumn{1}{|c|}{379} & 10 & \multicolumn{1}{|c|}{87} & \multicolumn{1}{|c|}{2303} & \multicolumn{1}{|c|}{60} & \multicolumn{1}{|c|}{1} \\ \hline
\multicolumn{1}{|c|}{380} & 10 & \multicolumn{1}{|c|}{130} & \multicolumn{1}{|c|}{2239} & \multicolumn{1}{|c|}{87} & \multicolumn{1}{|c|}{1} \\ \hline
\multicolumn{1}{|c|}{381} & 10 & \multicolumn{1}{|c|}{187} & \multicolumn{1}{|c|}{2175} & \multicolumn{1}{|c|}{130} & \multicolumn{1}{|c|}{1} \\ \hline
\multicolumn{1}{|c|}{382} & 10 & \multicolumn{1}{|c|}{250} & \multicolumn{1}{|c|}{2111} & \multicolumn{1}{|c|}{187} & \multicolumn{1}{|c|}{1} \\ \hline
\multicolumn{1}{|c|}{398} & 9 & \multicolumn{1}{|c|}{314} & \multicolumn{1}{|c|}{2047} & \multicolumn{1}{|c|}{250} & \multicolumn{1}{|c|}{1} \\ \hline
\multicolumn{1}{|c|}{406} & 9 & \multicolumn{1}{|c|}{2} & \multicolumn{1}{|c|}{1244} & \multicolumn{1}{|c|}{2} & \multicolumn{1}{|c|}{0} \\ \hline
\multicolumn{1}{|c|}{410} & 9 & \multicolumn{1}{|c|}{4} & \multicolumn{1}{|c|}{1243} & \multicolumn{1}{|c|}{4} & \multicolumn{1}{|c|}{0} \\ \hline
\multicolumn{2}{|c|}{\cellcolor[HTML]{FFFF00}\textbf{Base}}
& \multicolumn{2}{|c|}{\cellcolor[HTML]{FFFF00}\textbf{Transitive Closure}}
& \multicolumn{2}{|c|}{\cellcolor[HTML]{FFFF00}\textbf{Dominant Tree}} \\
\hline
\multicolumn{1}{|c|}{\textbf{Node}} & \multicolumn{1}{|c|}{\textbf{Value}}
& \multicolumn{1}{|c|}{\textbf{Node}} & \multicolumn{1}{|c|}{\textbf{Value}}
& \multicolumn{1}{|c|}{\textbf{Node}} & \multicolumn{1}{|c|}{\textbf{Value}}
\\ \hline
\multicolumn{1}{|c|}{314} & \multicolumn{1}{|c|}{11}
& \multicolumn{1}{|c|}{0} & \multicolumn{1}{|c|}{2490}
& \multicolumn{1}{|c|}{1} & \multicolumn{1}{|c|}{1246}
\\ \hline
\multicolumn{1}{|c|}{346} & \multicolumn{1}{|c|}{10}
& \multicolumn{1}{|c|}{1} & \multicolumn{1}{|c|}{2489}
& \multicolumn{1}{|c|}{3} & \multicolumn{1}{|c|}{934}
\\ \hline
\multicolumn{1}{|c|}{362} & \multicolumn{1}{|c|}{10}
& \multicolumn{1}{|c|}{3} & \multicolumn{1}{|c|}{2487}
& \multicolumn{1}{|c|}{7} & \multicolumn{1}{|c|}{156}
\\ \hline
\multicolumn{1}{|c|}{370} & \multicolumn{1}{|c|}{10}
& \multicolumn{1}{|c|}{7} & \multicolumn{1}{|c|}{2479}
& \multicolumn{1}{|c|}{42} & \multicolumn{1}{|c|}{115}
\\ \hline
\multicolumn{1}{|c|}{374} & \multicolumn{1}{|c|}{10}
& \multicolumn{1}{|c|}{15} & \multicolumn{1}{|c|}{2463}
& \multicolumn{1}{|c|}{314} & \multicolumn{1}{|c|}{31}
\\ \hline
\multicolumn{1}{|c|}{376} & \multicolumn{1}{|c|}{10}
& \multicolumn{1}{|c|}{27} & \multicolumn{1}{|c|}{2447}
& \multicolumn{1}{|c|}{0} & \multicolumn{1}{|c|}{1}
\\ \hline
\multicolumn{1}{|c|}{377} & \multicolumn{1}{|c|}{10}
& \multicolumn{1}{|c|}{42} & \multicolumn{1}{|c|}{2431}
& \multicolumn{1}{|c|}{15} & \multicolumn{1}{|c|}{1}
\\ \hline
\multicolumn{1}{|c|}{378} & \multicolumn{1}{|c|}{10}
& \multicolumn{1}{|c|}{60} & \multicolumn{1}{|c|}{2367}
& \multicolumn{1}{|c|}{27} & \multicolumn{1}{|c|}{1}
\\ \hline
\multicolumn{1}{|c|}{379} & \multicolumn{1}{|c|}{10}
& \multicolumn{1}{|c|}{87} & \multicolumn{1}{|c|}{2303}
& \multicolumn{1}{|c|}{60} & \multicolumn{1}{|c|}{1}
\\ \hline
\multicolumn{1}{|c|}{380} & \multicolumn{1}{|c|}{10}
& \multicolumn{1}{|c|}{130} & \multicolumn{1}{|c|}{2239}
& \multicolumn{1}{|c|}{87} & \multicolumn{1}{|c|}{1}
\\ \hline
\multicolumn{1}{|c|}{381} & \multicolumn{1}{|c|}{10}
& \multicolumn{1}{|c|}{187} & \multicolumn{1}{|c|}{2175}
& \multicolumn{1}{|c|}{130} & \multicolumn{1}{|c|}{1}
\\ \hline
\multicolumn{1}{|c|}{382} & \multicolumn{1}{|c|}{10}
& \multicolumn{1}{|c|}{250} & \multicolumn{1}{|c|}{2111}
& \multicolumn{1}{|c|}{187} & \multicolumn{1}{|c|}{1}
\\ \hline
\multicolumn{1}{|c|}{398} & \multicolumn{1}{|c|}{9}
& \multicolumn{1}{|c|}{314} & \multicolumn{1}{|c|}{2047}
& \multicolumn{1}{|c|}{250} & \multicolumn{1}{|c|}{1}
\\ \hline
\multicolumn{1}{|c|}{406} & \multicolumn{1}{|c|}{9}
& \multicolumn{1}{|c|}{2} & \multicolumn{1}{|c|}{1244}
& \multicolumn{1}{|c|}{2} & \multicolumn{1}{|c|}{0}
\\ \hline
\multicolumn{1}{|c|}{410} & \multicolumn{1}{|c|}{9}
& \multicolumn{1}{|c|}{4} & \multicolumn{1}{|c|}{1243}
& \multicolumn{1}{|c|}{4} & \multicolumn{1}{|c|}{0}
\\ \hline
\end{tabular}
\caption{Top 15 Nodes with Degree Centrality}
\label{table:car-deg}
@ -201,23 +297,92 @@ In this section, only results for the car network are displayed for brevity. The
\centering
\begin{tabular}{|cc|cc|cc|}
\hline
\multicolumn{2}{|c|}{\cellcolor[HTML]{FFFF00}\textbf{Base}} & \multicolumn{2}{|c|}{\cellcolor[HTML]{FFFF00}\textbf{Transitive Closure}} & \multicolumn{2}{|c|}{\cellcolor[HTML]{FFFF00}\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} & 0.002459349 & \multicolumn{1}{|c|}{0} & 74.447935 & \multicolumn{1}{|c|}{1} & 0.0542337315 \\ \hline
\multicolumn{1}{|c|}{377} & 0.001870821 & \multicolumn{1}{|c|}{1} & 67.679941 & \multicolumn{1}{|c|}{3} & 0.0385235854 \\ \hline
\multicolumn{1}{|c|}{346} & 0.001870821 & \multicolumn{1}{|c|}{3} & 60.55317 & \multicolumn{1}{|c|}{7} & 0.0066730273 \\ \hline
\multicolumn{1}{|c|}{376} & 0.001870821 & \multicolumn{1}{|c|}{7} & 51.894146 & \multicolumn{1}{|c|}{0} & 0.0058248184 \\ \hline
\multicolumn{1}{|c|}{374} & 0.001870821 & \multicolumn{1}{|c|}{15} & 43.13118 & \multicolumn{1}{|c|}{42} & 0.0050225267 \\ \hline
\multicolumn{1}{|c|}{378} & 0.001870821 & \multicolumn{1}{|c|}{27} & 35.752083 & \multicolumn{1}{|c|}{314} & 0.0016459253 \\ \hline
\multicolumn{1}{|c|}{380} & 0.001870821 & \multicolumn{1}{|c|}{42} & 29.550411 & \multicolumn{1}{|c|}{27} & 0.0009036979 \\ \hline
\multicolumn{1}{|c|}{381} & 0.001870821 & \multicolumn{1}{|c|}{60} & 22.205831 & \multicolumn{1}{|c|}{250} & 0.0005660377 \\ \hline
\multicolumn{1}{|c|}{382} & 0.001870821 & \multicolumn{1}{|c|}{87} & 16.522142 & \multicolumn{1}{|c|}{15} & 0.000491815 \\ \hline
\multicolumn{1}{|c|}{262} & 0.001870821 & \multicolumn{1}{|c|}{130} & 12.155237 & \multicolumn{1}{|c|}{187} & 0.000458049 \\ \hline
\multicolumn{1}{|c|}{370} & 0.001870821 & \multicolumn{1}{|c|}{2} & 10.714534 & \multicolumn{1}{|c|}{130} & 0.0004472501 \\ \hline
\multicolumn{1}{|c|}{379} & 0.001870821 & \multicolumn{1}{|c|}{4} & 9.740485 & \multicolumn{1}{|c|}{87} & 0.0004461702 \\ \hline
\multicolumn{1}{|c|}{418} & 0.001469376 & \multicolumn{1}{|c|}{5} & 9.740485 & \multicolumn{1}{|c|}{60} & 0.0004460622 \\ \hline
\multicolumn{1}{|c|}{459} & 0.001469376 & \multicolumn{1}{|c|}{6} & 9.740485 & \multicolumn{1}{|c|}{2} & 0.0004014452 \\ \hline
\multicolumn{1}{|c|}{467} & 0.001469376 & \multicolumn{1}{|c|}{187} & 8.82693 & \multicolumn{1}{|c|}{4} & 0.0004014452 \\ \hline
\multicolumn{2}{|c|}{\cellcolor[HTML]{FFFF00}\textbf{Base}}
& \multicolumn{2}{|c|}{\cellcolor[HTML]{FFFF00}\textbf{Transitive Closure}}
& \multicolumn{2}{|c|}{\cellcolor[HTML]{FFFF00}\textbf{Dominant Tree}}
\\ \hline
\multicolumn{1}{|c|}{\textbf{Node}} & \multicolumn{1}{|c|}{\textbf{Value}}
& \multicolumn{1}{|c|}{\textbf{Node}} & \multicolumn{1}{|c|}{\textbf{Value}}
& \multicolumn{1}{|c|}{\textbf{Node}} & \multicolumn{1}{|c|}{\textbf{Value}}
\\ \hline
\multicolumn{1}{|c|}{314} & \multicolumn{1}{|c|}{0.002459349}
& \multicolumn{1}{|c|}{0} & \multicolumn{1}{|c|}{74.447935}
& \multicolumn{1}{|c|}{1} & \multicolumn{1}{|c|}{0.0542337315}
\\ \hline
\multicolumn{1}{|c|}{377} & \multicolumn{1}{|c|}{0.001870821}
& \multicolumn{1}{|c|}{1} & \multicolumn{1}{|c|}{67.679941}
& \multicolumn{1}{|c|}{3} & \multicolumn{1}{|c|}{0.0385235854}
\\ \hline
\multicolumn{1}{|c|}{346} & \multicolumn{1}{|c|}{0.001870821}
& \multicolumn{1}{|c|}{3} & \multicolumn{1}{|c|}{60.55317}
& \multicolumn{1}{|c|}{7} & \multicolumn{1}{|c|}{0.0066730273}
\\ \hline
\multicolumn{1}{|c|}{376} & \multicolumn{1}{|c|}{0.001870821}
& \multicolumn{1}{|c|}{7} & \multicolumn{1}{|c|}{51.894146}
& \multicolumn{1}{|c|}{0} & \multicolumn{1}{|c|}{0.0058248184}
\\ \hline
\multicolumn{1}{|c|}{374} & \multicolumn{1}{|c|}{0.001870821}
& \multicolumn{1}{|c|}{15} & \multicolumn{1}{|c|}{43.13118}
& \multicolumn{1}{|c|}{42} & \multicolumn{1}{|c|}{0.0050225267}
\\ \hline
\multicolumn{1}{|c|}{378} & \multicolumn{1}{|c|}{0.001870821}
& \multicolumn{1}{|c|}{27} & \multicolumn{1}{|c|}{35.752083}
& \multicolumn{1}{|c|}{314} & \multicolumn{1}{|c|}{0.0016459253}
\\ \hline
\multicolumn{1}{|c|}{380} & \multicolumn{1}{|c|}{0.001870821}
& \multicolumn{1}{|c|}{42} & \multicolumn{1}{|c|}{29.550411}
& \multicolumn{1}{|c|}{27} & \multicolumn{1}{|c|}{0.0009036979}
\\ \hline
\multicolumn{1}{|c|}{381} & \multicolumn{1}{|c|}{0.001870821}
& \multicolumn{1}{|c|}{60} & \multicolumn{1}{|c|}{22.205831}
& \multicolumn{1}{|c|}{250} & \multicolumn{1}{|c|}{0.0005660377}
\\ \hline
\multicolumn{1}{|c|}{382} & \multicolumn{1}{|c|}{0.001870821}
& \multicolumn{1}{|c|}{87} & \multicolumn{1}{|c|}{16.522142}
& \multicolumn{1}{|c|}{15} & \multicolumn{1}{|c|}{0.000491815}
\\ \hline
\multicolumn{1}{|c|}{262} & \multicolumn{1}{|c|}{0.001870821}
& \multicolumn{1}{|c|}{130} & \multicolumn{1}{|c|}{12.155237}
& \multicolumn{1}{|c|}{187} & \multicolumn{1}{|c|}{0.000458049}
\\ \hline
\multicolumn{1}{|c|}{370} & \multicolumn{1}{|c|}{0.001870821}
& \multicolumn{1}{|c|}{2} & \multicolumn{1}{|c|}{10.714534}
& \multicolumn{1}{|c|}{130} & \multicolumn{1}{|c|}{0.0004472501}
\\ \hline
\multicolumn{1}{|c|}{379} & \multicolumn{1}{|c|}{0.001870821}
& \multicolumn{1}{|c|}{4} & \multicolumn{1}{|c|}{9.740485}
& \multicolumn{1}{|c|}{87} & \multicolumn{1}{|c|}{0.0004461702}
\\ \hline
\multicolumn{1}{|c|}{418} &\multicolumn{1}{|c|}{0.001469376}
& \multicolumn{1}{|c|}{5} & \multicolumn{1}{|c|}{9.740485}
& \multicolumn{1}{|c|}{60} & \multicolumn{1}{|c|}{0.0004460622}
\\ \hline
\multicolumn{1}{|c|}{459} & \multicolumn{1}{|c|}{0.001469376}
& \multicolumn{1}{|c|}{6} & \multicolumn{1}{|c|}{9.740485}
& \multicolumn{1}{|c|}{2} & \multicolumn{1}{|c|}{0.0004014452}
\\ \hline
\multicolumn{1}{|c|}{467} & \multicolumn{1}{|c|}{0.001469376}
& \multicolumn{1}{|c|}{187} & \multicolumn{1}{|c|}{8.82693}
& \multicolumn{1}{|c|}{4} & \multicolumn{1}{|c|}{0.0004014452}
\\ \hline
\end{tabular}
\caption{Top 15 Nodes with Katz Centrality}
\label{table:car-katz}