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The \emph{diameter} of a graph is the maximal distance between any two nodes related by a path.  A \emph{cycle} is a path of length $k$ such that $i_1=i_k$.   A set of nodes $S\subseteq \N$ is said to be:  \begin{itemize}[noitemsep] %\begin{itemize}[noitemsep]  \begin{itemize}  \item[]\emph{connected} if for any $i , j \in S$: $i R^{*}j$,   \item[] \emph{strongly connected} if for any $i,j \in S$: there is a path $\tuple{i,\dots, j}$,   \item[]\emph{closed} if for any $i\in S$, $j \notin S$, it is not the case that $iRj$,