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mp1: done 1-4 except 1.1

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Claudio Maggioni 2020-09-20 17:43:57 +02:00
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@ -61,7 +61,11 @@ is the corresponding eigenvalue, while if $x$ is an eigenvector approximation, f
The provided PageRank MATLAB implementation was run 3 times on the starting websites \texttt{http://atelier.inf.usi.ch/~maggicl}, \texttt{https://www.iisbadoni.edu.it}, and \texttt{https://www.usi.ch}, with results listed respectively in Figure \ref{fig:run1}, Figure \ref{fig:run2} and Figure \ref{fig:run3}. The provided PageRank MATLAB implementation was run 3 times on the starting websites \texttt{http://atelier.inf.usi.ch/~maggicl}, \texttt{https://www.iisbadoni.edu.it}, and \texttt{https://www.usi.ch}, with results listed respectively in Figure \ref{fig:run1}, Figure \ref{fig:run2} and Figure \ref{fig:run3}.
One patten that emerges on the first and third execution is the presence of 1s in the main diagonal. This indicates that several pages found have a link to themselves. Another interesting pattern, this time observable in all executions, is the presence of contiguous rectangular regions filled with 1s, especially along the main diagonal. This may be due to the presence of pages belonging to the same website, thus having a common layout and perhaps linking to a common set of internal (when near to the main diagonal) or external pages. One patten that emerges on the first and third execution is the presence of 1s in the main diagonal. This indicates that several pages found have a link to themselves.
Another interesting pattern, this time observable in all executions, is the presence of contiguous rectangular regions filled with 1s, especially along the main diagonal. This may be due to the presence of pages belonging to the same website, thus having a common layout and perhaps linking to a common set of internal (when near to the main diagonal) or external pages.
Finally, we can always observe a line starting from the top-left of G and ending in its bottom-left, running along a steep path slighly going right. This may be a side effect of the way pages are discovered and numbered: if new pages are continuously discovered, these pages will be added at the end of U and a corresponding vertical strip on 1s will appear in the bottomest non-colored region of G. This continues until $n$ unique pages are visited and the line reaches the bottom edge of the connectivity matrix. The steepness of the line thus formed depends on the amount of new pages discovered in each of the first iterations of the \texttt{surfer(...)} function.
\begin{figure}[h] \begin{figure}[h]
\centering \centering
@ -164,6 +168,22 @@ One patten that emerges on the first and third execution is the presence of 1s i
\subsection{Connectivity matrix and subcliques [10 points]} \subsection{Connectivity matrix and subcliques [10 points]}
The following ETH organization are following for the near cliques along the diagonal of the connectivity matrix in \texttt{eth500.mat}. The clique approximate position on the diagonal is indicated throgh the ranges in parenthesis.
\begin{itemize}
\item \texttt{baug.ethz.ch} (74-100)
\item \texttt{mat.ethz.ch} (114-129)
\item \texttt{mavt.ethz.ch} (164-182)
\item \texttt{biol.ethz.ch} (198-216)
\item \texttt{chab.ethz.ch} (221-236)
\item \texttt{math.ethz.ch} (264-278)
\item \texttt{erdw.ethz.ch} (321-337)
\item \texttt{usys.ethz.ch} (358-373)
\item \texttt{mtec.ethz.ch} (396-416)
\item \texttt{gess.ethz.ch} (436-462)
\end{itemize}
\subsection{Connectivity matrix and disjoint subgraphs [10 points]} \subsection{Connectivity matrix and disjoint subgraphs [10 points]}
\subsubsection{What is the connectivity matrix G (w.r.t figure 5)?} \subsubsection{What is the connectivity matrix G (w.r.t figure 5)?}