vrproject

pres1.tex (7850B)

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         \Large \emph{To be continued\ldots}
 
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         \Large \emph{Thank You!}
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 \title
 {Complex Network Analysis}
 \subtitle{Seminar, Project}
 \author[Popović Milutin]
 {Popović Milutin}
 \date{17. March 2021}
 
 \begin{document}
     \begin{frame}
         \titlepage
     \end{frame}
 
     \begin{frame}
         \begin{figure}[H]
             \centering
             \includegraphics[width=1.1\textwidth,
                              clip,
                              trim=0cm 10cm 0cm 7cm]
                              {./pics/code_example.pdf}
         \end{figure}
     \end{frame}
 
     \begin{frame}
         \centering
         \texttt{\$ pip install networkx}
         \vspace{1cm}
     \end{frame}
 
     \begin{frame}
         \centering
         \texttt{\$ pip install networkx}
         \vspace{1cm}
         \begin{itemize}
             \item[$\to$] Go to PyPi (Python Package Index) and download \&
                 install \texttt{networkx}
         \end{itemize}
     \end{frame}
 
     \begin{frame}
         \begin{figure}[H]
             \centering
             \includegraphics[width=1.1\textwidth,
                              clip,
                              trim=0cm 10cm 0cm 7cm]
                              {./pics/code_example.pdf}
         \end{figure}
     \end{frame}
 
     \begin{frame}
         \begin{figure}[H]
             \centering
             \includegraphics[width=0.8\textwidth]
                              {./pics/pypi.png}
         \end{figure}
     \end{frame}
 
     \begin{frame}
         \begin{columns}[T]
             \column{0.4\textwidth}
         \begin{align*}
             \text{Nodes}\ &\to\  \text{Repositories}\\
             \text{Edges}\ &\to\ \text{Requirements}(Imoprts)
         \end{align*}
         \end{columns}
     \end{frame}
 
     \begin{frame}
         \begin{columns}[T]
         \centering
             \column{0.4\textwidth}
         \begin{block}{\centering Directed Graph}
             \centering \texttt{scipy $\to$ numpy}\\
         \end{block}
         \end{columns}
     \end{frame}
 
     \begin{frame}
         \begin{columns}[T]
         \centering
             \column{0.4\textwidth}
         \begin{block}{\centering Directed Graph}
             \centering \texttt{scipy $\to$ numpy}\\
             \centering \texttt{scipy $\not\gets$ numpy}
         \end{block}
         \end{columns}
     \end{frame}
 
     \begin{frame}
         \centering
         \texttt{DiGraph with 361,742 nodes and 719,797 edges}\\
         \vspace{1cm}
     \end{frame}
 
     \begin{frame}
         \centering
         \texttt{DiGraph with 361,742 nodes and 719,797 edges}\\
         \vspace{1cm}
         \begin{itemize}
             \item[$\to$]\centering $\sim$362,000 out of $\sim$363,000  (Not what I expected)!
         \end{itemize}
     \end{frame}
 
     \begin{frame}
         \centering
         \texttt{DiGraph with 361,742 nodes and 719,797 edges}\\
         \vspace{1cm}
         \begin{itemize}
             \item[$\to$]\centering $\sim$362,000 out of $\sim$363,000  (Not what I expected)!
             \item[$\to$]\centering Significant data has $k_i > 0$ $\to$
                                $\sim$164,000 nodes and $\sim$720,000 edges
         \end{itemize}
     \end{frame}
 
     \begin{frame}
         \frametitle{Plotting Dependencies}
     \begin{figure}[htpb]
         \centering
         \includegraphics[width=1\textwidth, ]{./pics/req_3d.png}
         \caption{Plot of the Python Dependencies Network $k_{\text{in}}\ge
             10$, $N=4826$, $L=20847$
             (red nodes indicate high degree)}
     \end{figure}
     \end{frame}
 
     \begin{frame}
         \frametitle{Network Information}
       \begin{columns}[T]
         \column{0.4\textwidth}
             \begin{block}{\centering Basic Properties}
                 \begin{align*}
                    \quad\qquad \langle k_{\text{in}}\rangle  &= 1.99\\
                    \quad\qquad \langle k_{\text{out}}\rangle  &= 1.99\\
                    \quad\qquad \langle k\rangle  &= 8.75\\
                    \quad\qquad \langle k^2\rangle  &=\ -
                 \end{align*}
           \end{block}
 
         \column{0.54\textwidth}
         \begin{block}{\centering Specific Properties}
                 \begin{align*}
                     S &\simeq 1 \hspace{1.7cm} Connected\\
                       \langle d_\text{min}\rangle  &= 7.63 \qquad
                       \text{Small-World}\\
                       d_{\text{max}} &= 18.09\\
                       r &= -0.125 \qquad \text{Assortative}\\
                 \end{align*}
         \end{block}
         \end{columns}
     \end{frame}
 
     \begin{frame}
         \frametitle{Undirected Degree Distribution}
     \begin{figure}[htpb]
         \centering
         \includegraphics[width=1\textwidth]{./pics/dist_u.png}
         \caption{Undirected (left) distribution $p_k$ (right) cumulative
         degree distribution with fit for $k > 0$}
     \end{figure}
     \end{frame}
 
     \begin{frame}
         \frametitle{Directed Degree Distribution}
     \begin{figure}[htpb]
         \centering
         \includegraphics[width=1\textwidth]{./pics/dist_d.png}
         \caption{Directed (left) distribution $p_k$ (right) cumulative
         degree distribution with fit for $k > 0$}
     \end{figure}
     \end{frame}
 
     \begin{frame}
         \frametitle{Community Detection}
         \begin{columns}[T]
         \column{0.4\textwidth}
         \begin{block}{\centering Louvain-Algorithm}
             \centering
             Optimize \textbf{Modularity} $M$\\
             $O(L)$
         \end{block}
         \column{0.4\textwidth}
         \begin{block}{\centering Info-Map-Algorithm}
             \centering
             Optimize \textbf{Map-Equation} $\mathcal{L}$\\
             $O(N\log(N))$
         \end{block}
         \end{columns}
         \vspace{1cm}
     \end{frame}
 
     \begin{frame}
         \frametitle{Community Detection}
         \begin{columns}[T]
         \column{0.4\textwidth}
         \begin{block}{\centering Louvain-Algorithm}
             \centering
             Optimize \textbf{Modularity} $M$\\
             $O(N)$
         \end{block}
         \column{0.4\textwidth}
         \begin{block}{\centering Info-Map-Algorithm}
             \centering
             Optimize \textbf{Map-Equation} $\mathcal{L}$\\
             $O(N\log(N)$
         \end{block}
         \end{columns}
         \vspace{1cm}
         \begin{itemize}
             \item[$\to$]\centering Detect \& Analyze Community Structure
         \end{itemize}
     \end{frame}
 
     \begin{frame}
         \frametitle{Sneak Preview}
         \begin{figure}[htpb]
             \centering
             \includegraphics[width=1\textwidth]{./pics/sneak_peak.png}
             \label{fig:-frac-pics-sneap_peak-png}
         \end{figure}
     \end{frame}
 
     \begin{frame}{Bibliography}
         \nocite{barabasi}
         \nocite{motivation}
         \nocite{pypi}
         \printbibliography
     \end{frame}
 \end{document}