I don't understand why the only state with period > 1 is 1 Let's take state 2 for example, what's the period for state 2?
Another question is, does an absorbing state(state 4 in this example) only have period of 1?
2026-04-02 07:30:21.1775115021
periodic period for Markov Chain
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That's wrong (as you can tell from the fact that it's underlined in red ;-). All states except state $4$ have period $3$. The diagram is incomplete, since there are no transitions from state $4$; the statement "State $4$ is absorbing." implies that the missing transition is from $4$ to itself with probability $1$. Yes, an absorbing state has period $1$, since a return from that state to that state occurs in each step, so the period has to divide all natural numbers.