I am new to graph theory but I have some knowledge about Markov Chains.That is for example a state $j$ (vertex) is recurrent (strongly connected) if the Markov chain started in $j$ eventually revisits $j$.In graph theory they name it persistent.
In the other hand the state (vertex) $j$ is said to be transient if there is positive probability that the Markov chain started in $j$ never returns to $j$.
A Markov chain now is said to be irreducible if all the states all recurrent. So in the context of graph theory what does reducibility/irreducibility mean for directed graphs?
Can some please help me with that or indicate me a book that describes these two properties for directed graphs ?