pres2.tex (9579B)
1 \documentclass[fleqn]{beamer} 2 \beamertemplatenavigationsymbolsempty 3 4 \usepackage[T1]{fontenc} 5 \usepackage[utf8]{inputenc} 6 7 \usepackage{amsmath,amssymb} 8 \usepackage{graphicx} 9 \usepackage{mathptmx} 10 \usepackage{subcaption} 11 \usepackage{amsthm} 12 \usepackage{tikz} 13 %\usepackage[colorlinks=true,naturalnames=true,plainpages=false,pdfpagelabels=true]{hyperref} 14 \usetikzlibrary{patterns,decorations.pathmorphing,positioning, arrows, chains} 15 16 \usepackage[backend=biber, sorting=none]{biblatex} 17 \addbibresource{uni.bib} 18 19 \setbeamertemplate{endpage}{% 20 \begin{frame} 21 \centering 22 \Large \emph{To be continued\ldots} 23 24 \vspace{1cm} 25 26 \centering 27 \Large \emph{Thank You!} 28 \end{frame} 29 } 30 31 \AtEndDocument{\usebeamertemplate{endpage}} 32 33 % vertical separator macro 34 \newcommand{\vsep}{ 35 \column{0.0\textwidth} 36 \begin{tikzpicture} 37 \draw[very thick,black!10] (0,0) -- (0,7.3); 38 \end{tikzpicture} 39 } 40 \setlength{\mathindent}{0pt} 41 42 % Beamer theme 43 \usetheme{UniVienna} 44 \usefonttheme[onlysmall]{structurebold} 45 \mode<presentation> 46 \setbeamercovered{transparent=10} 47 48 \title 49 {Seminar Complex Network Analysis} 50 \subtitle{Project Progress} 51 \author[Popović Milutin] 52 {Popović Milutin} 53 \date{5. May 2021} 54 55 \begin{document} 56 \begin{frame} 57 \titlepage 58 \end{frame} 59 60 \begin{frame} 61 \frametitle{Reminder} 62 \centering 63 \textbf{Python Package Dependency Network} 64 \vspace{1cm} 65 \begin{columns}[T] 66 \column{0.4\textwidth} 67 \column{0.4\textwidth} 68 \end{columns} 69 \end{frame} 70 71 \begin{frame} 72 \frametitle{Reminder} 73 \centering 74 \textbf{Python Package Dependency Network} 75 \vspace{1cm} 76 \begin{columns}[T] 77 \column{0.4\textwidth} 78 \begin{align*} 79 \text{Nodes}\ &\to\ \text{Repositories}\\ 80 \text{Edges}\ &\to\ \text{Requirements}(Imoprts) 81 \end{align*} 82 \column{0.4\textwidth} 83 \end{columns} 84 \end{frame} 85 86 \begin{frame} 87 \frametitle{Reminder} 88 \centering 89 \textbf{Python Package Dependency Network} 90 \vspace{1cm} 91 \begin{columns}[T] 92 \column{0.4\textwidth} 93 \begin{align*} 94 \text{Nodes}\ &\to\ \text{Repositories}\\ 95 \text{Edges}\ &\to\ \text{Requirements}(Imoprts) 96 \end{align*} 97 \column{0.4\textwidth} 98 \begin{block}{\centering Directed Graph} 99 \centering \texttt{scipy $\to$ numpy}\\ 100 \centering \texttt{scipy $\not\gets$ numpy} 101 \end{block} 102 \end{columns} 103 \end{frame} 104 105 \begin{frame} 106 \frametitle{Revisiting the Data} 107 \begin{itemize} 108 \item[$\to$] Python Package Index (PyPi) gives release 109 information for every version of a package 110 \end{itemize} 111 \vspace{6cm} 112 \end{frame} 113 114 \begin{frame} 115 \frametitle{Revisiting the Data} 116 \begin{itemize} 117 \item[$\to$] Python Package Index (PyPi) gives release 118 information for every version of a package 119 \end{itemize} 120 \centering \textbf{requests=="0.10.0"} 121 \begin{figure} 122 \centering 123 \includegraphics[width=0.8\textwidth] 124 {./pics/json.png} 125 \end{figure} 126 \end{frame} 127 128 \begin{frame} 129 \frametitle{Revisiting the Data} 130 \begin{itemize} 131 \item[$\to$] Python Package Index (PyPi) gives release 132 information for every version of a package 133 \end{itemize} 134 \centering \textbf{requests=="0.10.0"} 135 \begin{figure} 136 \centering 137 \includegraphics[width=0.8\textwidth] 138 {./pics/select_json.png} 139 \end{figure} 140 \end{frame} 141 142 \begin{frame} 143 \frametitle{Revisiting The Data} 144 \begin{columns}[T] 145 \column{0.4\textwidth} 146 \begin{align*} 147 \to &\;\;\text{sort nodes \& links based on release date}\\ 148 &\Rightarrow\; \text{Time dependent directed network} 149 \end{align*} 150 \end{columns} 151 \end{frame} 152 153 \begin{frame} 154 \frametitle{Dealing with Time dependent Graphs} 155 \centering $\to$\;\; Child-Class of \texttt{nx.DiGraph}\\ 156 \vspace{4.2cm} 157 \end{frame} 158 159 \begin{frame} 160 \frametitle{Dealing with Time dependent Graphs} 161 \centering $\to$\;\; Child-Class of \texttt{nx.DiGraph}\\ 162 \centering $\to$\;\; Every edge has a time-stamp e.g.\\ 163 \vspace{0.5cm} 164 \centering \hspace{0.5cm} \texttt{scipy} $\rightarrow$ 165 \texttt{numpy} at $t = \text{2016-4}$ 166 \vspace{3cm} 167 \end{frame} 168 169 \begin{frame} 170 \frametitle{Dealing with Time dependent Graphs} 171 \centering $\to$\;\; Child-Class of \texttt{nx.DiGraph}\\ 172 \centering $\to$\;\; Every edge has a time-stamp e.g.\\ 173 \vspace{0.5cm} 174 \centering \hspace{0.5cm} \texttt{scipy} $\rightarrow$ 175 \texttt{numpy} at $t = \text{2016-4}$ 176 \vspace{1cm} 177 178 \centering \texttt{class TDiGraph(nx.DiGraph)} 179 \begin{columns}[T] 180 \column{0.45\textwidth} 181 \begin{block}{\centering Class Method: forward} 182 \centering add edges with time-stamp $t$\\ 183 \centering set $t = t + 1$ 184 \end{block} 185 \column{0.45\textwidth} 186 \end{columns} 187 \end{frame} 188 189 \begin{frame} 190 \frametitle{Dealing with Time dependent Graphs} 191 \centering $\to$\;\; Child-Class of \texttt{nx.DiGraph}\\ 192 \centering $\to$\;\; Every edge has a time-stamp e.g.\\ 193 \vspace{0.5cm} 194 \centering \hspace{0.5cm} \texttt{scipy} $\rightarrow$ 195 \texttt{numpy} at $t = \text{2016-4}$ 196 \vspace{1cm} 197 198 \centering \texttt{class TDiGraph(nx.DiGraph)} 199 \begin{columns}[T] 200 \column{0.45\textwidth} 201 \begin{block}{\centering Class Method: forward} 202 \centering add edges with time-stamp $t$\\ 203 \centering set $t = t + 1$ 204 \end{block} 205 \column{0.45\textwidth} 206 \begin{block}{\centering Class Method: backward } 207 \centering remove edges with time-stamp $t$\\ 208 \centering set $t = t - 1$ 209 \end{block} 210 \end{columns} 211 \end{frame} 212 213 \begin{frame} 214 \frametitle{Traveling Back in Time} 215 \begin{figure}[htpb] 216 \centering 217 \includegraphics[width=0.45\textwidth]{./pics/plot_2015.png} 218 \includegraphics[width=0.45\textwidth]{./pics/plot_sqrt.png} 219 \caption{Left: Graph from 2015, Right: Graph from 2022} 220 \end{figure} 221 \end{frame} 222 223 \begin{frame} 224 \frametitle{Observations} 225 \begin{figure}[htpb] 226 \centering 227 \includegraphics[width=0.8\textwidth]{./pics/edge_growth.png} 228 \caption{Growth-Exponent $\beta_i$ of the top nodes} 229 \end{figure} 230 \end{frame} 231 232 \begin{frame} 233 \frametitle{Observations} 234 \begin{figure}[htpb] 235 \centering 236 \includegraphics[width=0.8\textwidth]{./pics/fitness.png} 237 \caption{Distribution of the node fitness $\rho(\eta)$} 238 \end{figure} 239 \end{frame} 240 241 \begin{frame} 242 \frametitle{Visualizing the Network: Layout} 243 \centering \textbf{Idea: ``Light-Ray'' Layout} 244 \end{frame} 245 246 \begin{frame} 247 \frametitle{Visualizing the Network: Layout} 248 \centering \textbf{Idea: ``Light-Ray'' Layout} 249 \begin{itemize} 250 \item[$\to$] separate nodes based on their degree 251 \end{itemize} 252 \end{frame} 253 254 \begin{frame} 255 \frametitle{Visualizing the Network: Layout} 256 \centering \textbf{Idea: ``Light-Ray'' Layout} 257 \begin{itemize} 258 \item[$\to$] separate nodes based on their degree 259 \item[$\to$] place them each uniformly on a circle/disks 260 distance 261 \end{itemize} 262 \end{frame} 263 264 \begin{frame} 265 \frametitle{Visualizing the Network: Layout} 266 \centering \textbf{Idea: ``Light-Ray'' Layout} 267 \begin{itemize} 268 \item[$\to$] separate nodes based on their degree 269 \item[$\to$] place them each uniformly on a circle/disks 270 \item[$\to$] stack the disks, based on a function representing their 271 distance 272 \end{itemize} 273 \end{frame} 274 275 \begin{frame} 276 \frametitle{Visualizing the Network: Layout} 277 \begin{figure}[htpb] 278 \centering 279 \includegraphics[width=0.7\textwidth]{./pics/plot_sqrt.png} 280 \end{figure} 281 \end{frame} 282 283 \begin{frame} 284 \frametitle{Visualizing the Network: Layout} 285 \begin{figure}[htpb] 286 \centering 287 \includegraphics[width=0.7\textwidth]{./pics/plot_lin.png} 288 \end{figure} 289 \end{frame} 290 291 \begin{frame} 292 \frametitle{Visualizing the Network: Layout} 293 \begin{figure}[htpb] 294 \centering 295 \includegraphics[width=0.7\textwidth]{./pics/plot_exp.png} 296 \end{figure} 297 \end{frame} 298 299 \begin{frame} 300 \frametitle{Visualizing the Network: Layout} 301 \begin{figure}[htpb] 302 \centering 303 \includegraphics[width=0.7\textwidth]{./pics/plot_sin2.png} 304 \end{figure} 305 \end{frame} 306 307 \begin{frame}{Bibliography} 308 \nocite{barabasi} 309 \nocite{pypi} 310 \printbibliography 311 \end{frame} 312 \end{document} 313