LaTeX Forum

In Figure \ref{pagerankbeispielgraph}, you can see the graph that represents a set of linked documents. Each node represents one document. An edge between two nodes means, that the document from that the edge starts, links to the document into that the edge ends.\\
%%%%%%%%%%%%%Graph der Linkstruktur von 4 Dokumenten für PageRank%%%%%%%%%%%%%
\begin{figure}[h]
\centering
	\begin{tikzpicture}[->,>=stealth',shorten >=1pt,auto,node distance=2.8cm, semithick]
	\tikzstyle{every state}=[fill=red,draw=none,text=white]

	 \node[state]         (B) {$B$};
 	 \node[state]         (D) [below right of=B] {$D$};
 	 \node[state]         (C) [below left of=B] {$C$};
  	 \node[state]         (E) [below of=B]       {$E$};

  	 \path (C) edge              node {} (B)
	 	       edge	         node {} (D)
            	 (B) edge              node {} (C)
           	 (D) edge              node {} (B)
	 	       edge		node{} (E)
            	 (E) edge	         node {} (B);
\end{tikzpicture}
\caption{The link structure of 4 documents A,B,C and D represented as a graph}
\label{pagerankbeispielgraph}
\end{figure}
%%%%%%%%%%%%%Graph der Linkstruktur von 4 Dokumenten für PageRank%%%%%%%%%%%%%
As you can see in the figure, all documents link document B. It is obvious, that document B is important. One the other hand, B itself links only one document, namely document C. It is also obvious, that document C should also be important. When computing the PageRank for that example, the solution vector looks like this:\\

\documentclass[
	paper=a4,
	twoside=false,
	fontsize=11pt,
	parskip=false,
	]{scrartcl}
\usepackage{selinput}
\SelectInputMappings{adieresis={ä}, germandbls={ß},Euro={€}}
\usepackage[T1]{fontenc}
\usepackage[ngerman,]{babel}
\usepackage{microtype}
\usepackage{lmodern}
\usepackage{tikz}
\usetikzlibrary{arrows,automata}
\title{}
\author{}
\begin{document}
In Figure \ref{pagerankbeispielgraph}, you can see the graph that represents a set of linked documents. Each node represents one document. An edge between two nodes means, that the document from that the edge starts, links to the document into that the edge ends.\par
%%%%%%%%%%%%%Graph der Linkstruktur von 4 Dokumenten für PageRank%%%%%%%%%%%%%
\begin{figure}[h]
\centering
   \begin{tikzpicture}[->,>=stealth',shorten >=1pt,auto,node distance=2.8cm, semithick]
   \tikzstyle{every state}=[fill=red,draw=none,text=white]

    \node[state]         (B) {$B$};
     \node[state]         (D) [below right of=B] {$D$};
     \node[state]         (C) [below left of=B] {$C$};
      \node[state]         (E) [below of=B]       {$E$};

      \path (C) edge              node {} (B)
              edge            node {} (D)
                (B) edge              node {} (C)
               (D) edge              node {} (B)
              edge      node{} (E)
                (E) edge            node {} (B);
\end{tikzpicture}
\caption{The link structure of 4 documents A,B,C and D represented as a graph}
\label{pagerankbeispielgraph}
\end{figure}
%%%%%%%%%%%%%Graph der Linkstruktur von 4 Dokumenten für PageRank%%%%%%%%%%%%%
As you can see in the figure, all documents link document B. It is obvious, that document B is important. One the other hand, B itself links only one document, namely document C. It is also obvious, that document C should also be important. When computing the PageRank for that example, the solution vector looks like this:\\ 
\end{document}