
% this file is called up by thesis.tex
% content in this file will be fed into the main document

%: ----------------------- introduction file header -----------------------
\chapter{Additional experiments}\label{A:experiments}

Here, we present plots of of the intersection distances between the top 10 nodes, ranked by a variety of centrality measures, for a selection of real-world networks.  More details can be found in Chapter \ref{C:Robustness}.

\begin{figure}[t!]
\centering
\includegraphics[width=0.75\textwidth]{real_exp_diag_top10.eps}
\hspace{0.1in}
\includegraphics[width=0.75\textwidth]{real_exp_sum_top10.eps}
\caption{The intersection distances between the exponential subgraph centrality (left) or total communicability (right) rankings produced by successive choices of $\beta$ on the top 10 ranked nodes of each network. Each line corresponds to a network in Table \ref{tbl:basic_data}.}
\label{fig:real_exp_top10}
\end{figure} 

\begin{figure}[t!]
\centering
\includegraphics[width=0.75\textwidth]{real_res_diag_top10.eps}
\hspace{0.1in}
\includegraphics[width=0.75\textwidth]{real_res_sum_top10.eps}
\caption{The intersection distances between resolvent subgraph centrality (left) or Katz centrality (right) rankings produced by successive choices of $\alpha$ on the top 10 ranked nodes of each network.  Each line corresponds to a network in Table \ref{tbl:basic_data}.}
\label{fig:real_res_top10}
\end{figure}

\begin{figure}[t!]
\centering
%\includegraphics[width=0.75\textwidth]{real_exp_diag_top10_dir.eps}
%\hspace{0.1in}
\includegraphics[width=0.75\textwidth]{real_exp_sum_top10_dir.eps}
\caption{The intersection distances between the total communicability rankings of the top 10 nodes of each network produced by successive choices of $\beta$. Each line corresponds to a network in Table \ref{tbl:basic_data_dir}.}
\label{fig:real_exp_dir_top10}
\end{figure} 

\begin{figure}[t!]
\centering
%\includegraphics[width=0.75\textwidth]{real_res_diag_top10_dir.eps}
%\hspace{0.1in}
\includegraphics[width=0.75\textwidth]{real_res_sum_dir.eps}
\caption{The intersection distances between the Katz centrality rankings produced by successive choices of $\alpha$. Each line corresponds to a network in Table \ref{tbl:basic_data_dir}.}
\label{fig:real_res_top10_dir}
\end{figure} 

% the code below specifies where the figures are stored

%: ----------------------- HELP: references
% References can be links to figures, tables, sections, or references.
% For figures, tables, and text you define the target of the link with \label{XYZ}. Then you call cross-link with the command \ref{XYZ}, as above
% Citations are bound in a very similar way with \cite{XYZ}. You store your references in a BibTex file with a programme like BibDesk.

%\section{Motivation}
%%%%%%%%%%%%%%%%%%%%%%%%
%In this thesis we are interested in efficient methods for the numerical solution of saddle point systems arising from finite element discretization of two important classes of fluid dynamic problems, namely the \emph{incompressible Navier-Stokes equations} and the \emph{Brinkman equations}. 

%: ----------------------- HELP: adding figures with macros
% \figuremacro{1}{2}{3}{4} calls up a series of commands formating your image.
% 1 = name of the file without extension; PNG, JPEG is ok; GIF doesn't work
% 2 = title of the figure AND the name of the label for cross-linking
% 3 = caption text for the figure
% 4 = size relative to text width which is 1; use this to reduce figures




