Experimental Networks, starting centrality section

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Report/Bibliography.bib

@@ -1318,4 +1318,19 @@ of 27},
   year={2010},
   volume={432},
   pages={2181-2213}
+}
+
+@article {PMID:30064421,
+	Title = {A systematic survey of centrality measures for protein-protein interaction networks},
+	Author = {Ashtiani, Minoo and Salehzadeh-Yazdi, Ali and Razaghi-Moghadam, Zahra and Hennig, Holger and Wolkenhauer, Olaf and Mirzaie, Mehdi and Jafari, Mohieddin},
+	DOI = {10.1186/s12918-018-0598-2},
+	Number = {1},
+	Volume = {12},
+	Month = {July},
+	Year = {2018},
+	Journal = {BMC systems biology},
+	ISSN = {1752-0509},
+	Pages = {80},
+	Abstract = {<h4>Background</h4>Numerous centrality measures have been introduced to identify "central" nodes in large networks. The availability of a wide range of measures for ranking influential nodes leaves the user to decide which measure may best suit the analysis of a given network. The choice of a suitable measure is furthermore complicated by the impact of the network topology on ranking influential nodes by centrality measures. To approach this problem systematically, we examined the centrality profile of nodes of yeast protein-protein interaction networks (PPINs) in order to detect which centrality measure is succeeding in predicting influential proteins. We studied how different topological network features are reflected in a large set of commonly used centrality measures.<h4>Results</h4>We used yeast PPINs to compare 27 common of centrality measures. The measures characterize and assort influential nodes of the networks. We applied principal component analysis (PCA) and hierarchical clustering and found that the most informative measures depend on the network's topology. Interestingly, some measures had a high level of contribution in comparison to others in all PPINs, namely Latora closeness, Decay, Lin, Freeman closeness, Diffusion, Residual closeness and Average distance centralities.<h4>Conclusions</h4>The choice of a suitable set of centrality measures is crucial for inferring important functional properties of a network. We concluded that undertaking data reduction using unsupervised machine learning methods helps to choose appropriate variables (centrality measures). Hence, we proposed identifying the contribution proportions of the centrality measures with PCA as a prerequisite step of network analysis before inferring functional consequences, e.g., essentiality of a node.},
+	URL = {https://europepmc.org/articles/PMC6069823},
 }

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 \bibdata{Bibliography}
 \bibcite{phillips_graph-based_1998}{1}
 \bibcite{schneier_modeling_1999}{2}
@@ -44,6 +50,9 @@
 \bibcite{ming_diss}{7}
 \bibcite{Guo2017HermitianAM}{8}
 \bibcite{Brualdi2010SpectraOD}{9}
+\bibcite{noauthor_health_1996}{10}
+\bibcite{PCI}{11}
+\bibcite{PMID:30064421}{12}
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Report/Schrick-Noah_CS-7863_Final-Report.bbl

@@ -1,4 +1,4 @@
-\begin{thebibliography}{1}
+\begin{thebibliography}{10}
 
 \bibitem{phillips_graph-based_1998}
 C.~Phillips and L.~P. Swiler, ``A graph-based system for network-vulnerability
@@ -41,4 +41,21 @@ K.~Guo and B.~Mohar, ``Hermitian adjacency matrix of digraphs and mixed
 R.~A. Brualdi, ``Spectra of digraphs,'' {\em Linear Algebra and its
   Applications}, vol.~432, pp.~2181--2213, 2010.
 
+\bibitem{noauthor_health_1996}
+``Health {Insurance} {Portability} and {Accountability} {Act} of 1996.''
+\newblock Pub. L. No. 104-191. 1996 [Online]. Available:
+  https://www.govinfo.gov/content/pkg/PLAW-104publ191/html/PLAW-104publ191.htm.
+
+\bibitem{PCI}
+P.~S.~S. Council, ``Payment {Card} {Industry} {(PCI)} {Data} {Security}
+  {Standard},'' May 2018.
+\newblock {Available:
+  https://www.pcisecuritystandards.org/documents/PCI$\_$DSS$\_$v3-2-1.pdf}.
+
+\bibitem{PMID:30064421}
+M.~Ashtiani, A.~Salehzadeh-Yazdi, Z.~Razaghi-Moghadam, H.~Hennig,
+  O.~Wolkenhauer, M.~Mirzaie, and M.~Jafari, ``A systematic survey of
+  centrality measures for protein-protein interaction networks,'' {\em BMC
+  systems biology}, vol.~12, p.~80, July 2018.
+
 \end{thebibliography}

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Report/Schrick-Noah_CS-7863_Final-Report.tex

@@ -46,11 +46,26 @@ Analysis of directed graphs is not as simple as their undirected counterparts, a
 The author of \cite{ming_diss} presents three centrality measures that were applied to various attack graphs. The centrality measures implemented were Katz, K-path Edge, and Adapted PageRank. Each of these centrality measures are applicable to the directed format of attack graphs, and conclusions can be drawn regarding patching schemes for preventing exploits. As an approach for avoiding complex eigenvalues, the authors of \cite{Guo2017HermitianAM} present work examining directed, undirected, and mixed graphs using its Hermitian adjacency matrix. Other works, such as that discussed by the author of \cite{Mieghem2018DirectedGA} include mathematical manipulation of directed graph spectra (originally presented by the author of \cite{Brualdi2010SpectraOD}) with Schur's Theorem to bound eigenvalues and allow for explicit computation, which can then be used for additional analysis metrics. 
 
 \section{Experimental Networks}
-The work conducted in this approach
+The work conducted in this approach utilized three compliance graphs, with their properties displayed in Table \ref{table:networks}. Connectivity in this table refers to the mean degree, divided by the number of nodes in the network, multiplied by 100 to get the number in a percentage form. Network 1 is a vehicle maintenance network. This network has one car asset that is deemed ``brand new", and has no mileage. This network is examined at its current state, and progresses through time with time steps of 1 month, up to 12 months total. At each time step the car gains mileage and increases its age property, and is reexamined to evaluate its standing in regards to its vehicular regulatory maintenance schedule. Network 2 is an artificial company network that is attempting to maintain HIPAA compliance \cite{noauthor_health_1996}. This network examines its standing in relation to security properties that are required per HIPAA guidelines, as well as employee cooperation to training and administrative policies. This network is also progressed through time to illustrate the company's standing in relation to yearly audits and trainings that must be followed. Employees are also added and removed through the network at set points during the time progression process. Network 3 is another artificial company network. This company is attempting to maintain PCI DSS compliance \cite{PCI}. This network generation was static and did not progress through time. This network examined the company and its current state, and examined all changes that could occur. These changes were primarily tied to security properties such as physical break-ins on the property, firewalls being disabled, default system settings, and encryption expiration.
+
+\begin{table}[]
+    \centering
+    \begin{tabular}{|c|c|c|c|}
+    \hline
+    \textbf{Network} & \textbf{Nodes} & \textbf{Edges} & \textbf{Connectivity (\%)} \\  \hline
+    Car              &     2491       &  12968         &        0.209               \\  \hline
+    HIPAA            &     2321       &  8063          &        0.150               \\  \hline
+    PCI DSS          &     61         &  163           &        4.381               \\  \hline
+    \end{tabular}
+    \caption{Network Properties for the Three Networks Utilized}
+    \label{table:networks}
+\end{table}
 
 \section{Centralities}
 \subsection{Introduction}
+The author of \cite{PMID:30064421} provides a survey of centrality measures, and discusses how various centrality measures have been implemented and brought forth in order to determine node importance in networks. By determining the importance of nodes, various conclusions can be drawn regarding the network. In the case of compliance graphs, conclusions can be drawn regarding the prioritization of patching or correction schemes. If one node is known to lead to the creation of many other nodes, it may be said that a patch is imperative to prevent further opportunities for compliance violation. This work discusses five centrality measures, and discusses their application to compliance graphs.
 \subsection{Degree}
+Degree centrality is a trivial, localized measure of node importance based on the number of edges that a node has. In an undirected graph, the degree centrality is predicated solely on the number of edges. However, in the case of a directed graph, a distinction is drawn with a degree centrality oriented on the number of edges coming into a node, and another measure focused on the number of edges leaving a node. Both of these cases provide useful information for compliance graphs. When a node has a large number of other nodes it points to, this node may be prioritized since it creates further room for violation. When a node has a large number of edges pointing to it, this node may be prioritized since the probability that systems may enter this state is higher due to the increased number of ways that a system could lead to this state.
 \subsection{Betweenness}
 \subsection{Katz}
 \subsection{K-Path Edge}

Report/Schrick-Noah_CS-7863_Final-Report.toc

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 \contentsline {subsection}{\numberline {1.3}Difficulties of Compliance Graph Analysis}{3}{}%
 \contentsline {section}{\numberline {2}Related Works}{3}{}%
 \contentsline {section}{\numberline {3}Experimental Networks}{4}{}%
-\contentsline {section}{\numberline {4}Centralities}{5}{}%
-\contentsline {subsection}{\numberline {4.1}Introduction}{5}{}%
+\contentsline {section}{\numberline {4}Centralities}{4}{}%
+\contentsline {subsection}{\numberline {4.1}Introduction}{4}{}%
 \contentsline {subsection}{\numberline {4.2}Degree}{5}{}%
-\contentsline {subsection}{\numberline {4.3}Betweenness}{5}{}%
-\contentsline {subsection}{\numberline {4.4}Katz}{5}{}%
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-\contentsline {subsection}{\numberline {4.6}Adapted Page Rank}{5}{}%
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-\contentsline {subsection}{\numberline {5.1}Introduction}{5}{}%
-\contentsline {subsection}{\numberline {5.2}Application}{5}{}%
-\contentsline {section}{\numberline {6}Dominant Tree}{5}{}%
-\contentsline {subsection}{\numberline {6.1}Introduction}{5}{}%
-\contentsline {subsection}{\numberline {6.2}Application}{5}{}%
-\contentsline {section}{\numberline {7}Results and Result Analysis}{5}{}%
-\contentsline {section}{\numberline {8}Conclusions and Future Work}{5}{}%
-\contentsline {section}{Bibliography}{6}{}%
+\contentsline {subsection}{\numberline {4.3}Betweenness}{6}{}%
+\contentsline {subsection}{\numberline {4.4}Katz}{6}{}%
+\contentsline {subsection}{\numberline {4.5}K-Path Edge}{6}{}%
+\contentsline {subsection}{\numberline {4.6}Adapted Page Rank}{6}{}%
+\contentsline {section}{\numberline {5}Transitive Closure}{6}{}%
+\contentsline {subsection}{\numberline {5.1}Introduction}{6}{}%
+\contentsline {subsection}{\numberline {5.2}Application}{6}{}%
+\contentsline {section}{\numberline {6}Dominant Tree}{6}{}%
+\contentsline {subsection}{\numberline {6.1}Introduction}{6}{}%
+\contentsline {subsection}{\numberline {6.2}Application}{6}{}%
+\contentsline {section}{\numberline {7}Results and Result Analysis}{6}{}%
+\contentsline {section}{\numberline {8}Conclusions and Future Work}{6}{}%
+\contentsline {section}{Bibliography}{7}{}%