Table captions, unshading a figure, and adding 2 refs in future work

Bibliography.bib

@@ -277,4 +277,38 @@ doi = {https://doi.org/10.1016/j.amc.2017.10.001},
 url = {https://www.sciencedirect.com/science/article/pii/S0096300317306884},
 author = {Chao Li and Li Wang and Shiwen Sun and Chengyi Xia},
 keywords = {Influential spreaders, Identification algorithms, Classified neighbors, Complex networks},
-}
+}
+
+
+@Article{sym11020284,
+AUTHOR = {Agryzkov, Taras and Curado, Manuel and Pedroche, Francisco and Tortosa, Leandro and Vicent, José F.},
+TITLE = {Extending the Adapted PageRank Algorithm Centrality to Multiplex Networks with Data Using the PageRank Two-Layer Approach},
+JOURNAL = {Symmetry},
+VOLUME = {11},
+YEAR = {2019},
+NUMBER = {2},
+ARTICLE-NUMBER = {284},
+URL = {https://www.mdpi.com/2073-8994/11/2/284},
+ISSN = {2073-8994},
+ABSTRACT = {Usually, the nodes’ interactions in many complex networks need a more accurate mapping than simple links. For instance, in social networks, it may be possible to consider different relationships between people. This implies the use of different layers where the nodes are preserved and the relationships are diverse, that is, multiplex networks or biplex networks, for two layers. One major issue in complex networks is the centrality, which aims to classify the most relevant elements in a given system. One of these classic measures of centrality is based on the PageRank classification vector used initially in the Google search engine to order web pages. The PageRank model may be understood as a two-layer network where one layer represents the topology of the network and the other layer is related to teleportation between the nodes. This approach may be extended to define a centrality index for multiplex networks based on the PageRank vector concept. On the other hand, the adapted PageRank algorithm (APA) centrality constitutes a model to obtain the importance of the nodes in a spatial network with the presence of data (both real and virtual). Following the idea of the two-layer approach for PageRank centrality, we can consider the APA centrality under the perspective of a two-layer network where, on the one hand, we keep maintaining the layer of the topological connections of the nodes and, on the other hand, we consider a data layer associated with the network. Following a similar reasoning, we are able to extend the APA model to spatial networks with different layers. The aim of this paper is to propose a centrality measure for biplex networks that extends the adapted PageRank algorithm centrality for spatial networks with data to the PageRank two-layer approach. Finally, we show an example where the ability to analyze data referring to a group of people from different aspects and using different sets of independent data are revealed.},
+DOI = {10.3390/sym11020284}
+}
+
+@article{10.1093/bioinformatics/bty965,
+    author = {Parvandeh, Saeid and McKinney, Brett A},
+    title = "{EpistasisRank and EpistasisKatz: interaction network centrality methods that integrate prior knowledge networks}",
+    journal = {Bioinformatics},
+    volume = {35},
+    number = {13},
+    pages = {2329-2331},
+    year = {2018},
+    month = {11},
+    abstract = "{An important challenge in gene expression analysis is to improve hub gene selection to enrich for biological relevance or improve classification accuracy for a given phenotype. In order to incorporate phenotypic context into co-expression, we recently developed an epistasis-expression network centrality method that blends the importance of gene–gene interactions (epistasis) and main effects of genes. Further blending of prior knowledge from functional interactions has the potential to enrich for relevant genes and stabilize classification.We develop two new expression-epistasis centrality methods that incorporate interaction prior knowledge. The first extends our SNPrank (EpistasisRank) method by incorporating a gene-wise prior knowledge vector. This prior knowledge vector informs the centrality algorithm of the inclination of a gene to be involved in interactions by incorporating functional interaction information from the Integrative Multi-species Prediction database. The second method extends Katz centrality to expression-epistasis networks (EpistasisKatz), extends the Katz bias to be a gene-wise vector of main effects and extends the Katz attenuation constant prefactor to be a prior-knowledge vector for interactions. Using independent microarray studies of major depressive disorder, we find that including prior knowledge in network centrality feature selection stabilizes the training classification and reduces over-fitting.Methods and examples provided at https://github.com/insilico/Rinbix and https://github.com/insilico/PriorKnowledgeEpistasisRank.Supplementary data are available at Bioinformatics online.}",
+    issn = {1367-4803},
+    doi = {10.1093/bioinformatics/bty965},
+    url = {https://doi.org/10.1093/bioinformatics/bty965},
+    eprint = {https://academic.oup.com/bioinformatics/article-pdf/35/13/2329/36613945/bioinformatics\_35\_13\_2329.pdf},
+}
+
+
+

Schrick-Noah_CG-Network_Theory.aux

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 \newlabel{table:car-betweenness}{{VI}{6}}
 \citation{LI2018512}
 \citation{MO2019121538}
+\citation{sym11020284}
+\citation{10.1093/bioinformatics/bty965}
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 \bibdata{Bibliography}
 \bibcite{j_hale_compliance_nodate}{1}
 \bibcite{baloyi_guidelines_2019}{2}
@@ -91,15 +96,14 @@
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 \bibcite{dominance}{22}
 \bibcite{LI2018512}{23}
 \bibcite{MO2019121538}{24}
+\bibcite{sym11020284}{25}
+\bibcite{10.1093/bioinformatics/bty965}{26}
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Schrick-Noah_CG-Network_Theory.bbl

@@ -116,4 +116,15 @@ H.~Mo and Y.~Deng, ``Identifying node importance based on evidence theory in
   complex networks,'' {\em Physica A: Statistical Mechanics and its
   Applications}, vol.~529, p.~121538, 2019.
 
+\bibitem{sym11020284}
+T.~Agryzkov, M.~Curado, F.~Pedroche, L.~Tortosa, and J.~F. Vicent, ``Extending
+  the adapted pagerank algorithm centrality to multiplex networks with data
+  using the pagerank two-layer approach,'' {\em Symmetry}, vol.~11, no.~2,
+  2019.
+
+\bibitem{10.1093/bioinformatics/bty965}
+S.~Parvandeh and B.~A. McKinney, ``{EpistasisRank and EpistasisKatz:
+  interaction network centrality methods that integrate prior knowledge
+  networks},'' {\em Bioinformatics}, vol.~35, pp.~2329--2331, 11 2018.
+
 \end{thebibliography}

Schrick-Noah_CG-Network_Theory.blg

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Schrick-Noah_CG-Network_Theory.tex

@@ -96,7 +96,7 @@ The work conducted in this approach utilized three compliance graphs, with their
     HIPAA            &     2321       &  8063          &        0.150               \\  \hline
     PCI DSS          &     61         &  163           &        4.381               \\  \hline
     \end{tabular}
-    \caption{Network Properties for the Three Networks Utilized}
+    \caption{Network Structural Properties for the Three Example Networks Used}
     \label{table:networks}
 \end{table}
 
@@ -168,7 +168,7 @@ Section \ref{sec:networks}, and this transitive closure was then analyzed throug
     \includegraphics[scale=0.6]{"./images/TC.png"}
     \centering
     \vspace{.2truein} \centerline{}
-        \caption{Transitive Closure Illustration}
+        \caption{Illustration of an Example DAG and its Transitive Closure}
         \label{fig:TC}
 \end{figure}
 
@@ -179,14 +179,14 @@ Dominance, as initially introduced by the author of \cite{dominance} in terms of
 Following the properties of dominance, a dominator tree can be derived. In a dominator tree, each node has children that it immediately dominates. Immediate dominance is referred to nodes that strictly dominate a given node, but do not strictly dominate any other node that may strictly dominate a node. Figure 3 displays the dominant tree of the network seen in Figure 2.
 
 \begin{figure}[htp]
-    \includegraphics[scale=0.6]{"./images/dom_net.png"}
+    \includegraphics[scale=0.6]{"./images/dom_net_unshaded.png"}
     \centering
     \vspace{.2truein} \centerline{}
         \caption{Example Network for Illustrating Dominance}\label{fig:domNet}
 \end{figure}
 
 \begin{figure}[htp] 
-    \includegraphics[scale=0.6]{"./images/dom_tree.png"}
+    \includegraphics[scale=0.6]{"./images/dom_tree_unshaded.png"}
     \centering
     \vspace{.2truein} \centerline{}
         \caption{Dominant Tree Derived from the Network Displayed in Figure \ref{fig:domNet}}\label{fig:domTree}
@@ -227,7 +227,7 @@ In this section, only results for the car network are displayed for brevity. The
     \multicolumn{1}{|c|}{410}             & 0.07                & \multicolumn{1}{c|}{4}                      & 0.33                       & \multicolumn{1}{c|}{4}                    & 0.00                    \\ \hline
 
     \end{tabular}
-    \caption{Top 15 Nodes with Degree Centrality}
+    \caption{Top 15 Nodes with Degree 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-deg}
 \end{table}
 
@@ -260,7 +260,7 @@ In this section, only results for the car network are displayed for brevity. The
     \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}
+    \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}
 
@@ -293,7 +293,7 @@ In this section, only results for the car network are displayed for brevity. The
     \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}
+    \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}
 
@@ -326,7 +326,7 @@ In this section, only results for the car network are displayed for brevity. The
     \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}
+    \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}
 
@@ -359,7 +359,7 @@ In this section, only results for the car network are displayed for brevity. The
     \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}
+    \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}
 
@@ -377,7 +377,7 @@ Each centrality measure implemented in this work provides various information th
 \subsection{Future Work}
 Based on the results of this work, there is considerable opportunity to continue investigation of centrality methods for compliance graphs. With three compliance graphs generated for three different applications, along with various node importance rankings, it would be useful to artificially implement correction schemes based on the rankings to see their effects on the compliance graph. Extensions to the ranking and correction schemes could be made by creating a single source of importance ranking by collapsing or combining the vector of centrality method rankings. Since each centrality method highlights unique properties of the network, it may be useful to take each into consideration and determine a final, overall importance ranking. This approach has been seen in works such as those presented by the authors of \cite{LI2018512} and \cite{MO2019121538}.
 
-Further research could examine how node importance varies based on user-defined metrics by using a user-defined data matrix in centrality methods like PageRank. Edge weights could also be assigned to the original compliance graphs to represent the probability that a given change in the network could occur. Edge weights would be reflected in the adjacency matrices of the graphs, and centrality methods could be reexamined to determine node importance when state transition probabilities are given. Transitive closures and dominant trees derived from the compliance graphs present a new approach for examining compliance graphs. Further research can be conducted to determine the effects of correction schemes when employed on nodes ranked highly in their respective centrality measures in these formats.
+Further research could examine how node importance varies based on user-defined metrics by using a user-defined data matrix in centrality methods like PageRank. This approach has seen success through the work demonstrated by the authors of \cite{sym11020284}, which adds a data layer to the network for a two-layer approach to PageRank. Similar works can be seen by the authors of \cite{10.1093/bioinformatics/bty965}, which extends Katz to incorporate a prior knowledge vector. Edge weights could also be assigned to the original compliance graphs to represent the probability that a given change in the network could occur. Edge weights would be reflected in the adjacency matrices of the graphs, and centrality methods could be reexamined to determine node importance when state transition probabilities are given. Transitive closures and dominant trees derived from the compliance graphs present a new approach for examining compliance graphs. Further research can be conducted to determine the effects of correction schemes when employed on nodes ranked highly in their respective centrality measures in these formats.
 
 \addcontentsline{toc}{section}{Bibliography}
 \bibliography{Bibliography}