%\noindent $\sim_{d,T}$ is obviously an equivalence relation and when $d=1-\Delta$, where $\Delta$ is the similarity scoring function embedded into the emboss package , we will simply denote $\sim_{d,0.1}$ by $\sim$.
-Let be given a \emph{similarity} threshold $T$ and a distance $d$,
+Let be given a \emph{similarity} threshold $T$ and a distance $d$
(Needleman-Wunch released by EMBL for instance).
The method begins by building an undirected graph
between all the DNA~sequences $g$ of the set of genomes as follows:
This graph is further denoted as the ``similarity'' graph.
We thus consider that the pair of two coding sequences
-$(g_i,g_j)$ belongs in the relation $\mathcal{R}$ if both $g_i$ an,d
+$(g_i,g_j)$ belongs in the relation $\mathcal{R}$ if both $g_i$ and
$g_j$ belong in the same
connected component (CC), \textit{i.e.} if there is a path between $g_i$
-and $g_j$ in the similarity graph. It is not hard to see this relation is an
+and $g_j$ in the similarity graph. It is not hard to see that this relation is an
equivalence relation whereas $\sim$ is not.
\begin{figure}
\begin{center}
-\includegraphics[scale=0.4]{stats.png}
+\includegraphics[scale=0.5]{stats.png}
\end{center}
\caption{Size of core and pan genomes w.r.t. the similarity threshold}\label{Fig:sim:core:pan}
\end{figure}
