If we are given a markov chain and have to decide if states intercommunicate with one another, do we need to consider a state communicating with itself.
E.g. with $$ \begin{matrix} 0.3 & 0 & 0.7 \\ 0 & 0.5 & 0.5 \\ 0.5 & 0.5 & 0 \\ \end{matrix} $$ it is clear $1 \rightarrow 2$, $2 \rightarrow 3$ and so on... . But, do we need to say that $1 \rightarrow 1$, $2 \rightarrow 2$ and $3 \rightarrow 3$
I have never seen it written in an example nor does the definition suggest we should consider it. So, is it just always the case that states communicate with themselves?