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If these arrows are weight by probabilities, then the above construction produces a [Markov chain](https://en.wikipedia.org/wiki/Markov_chain).

So the number of arrow or morphisms of a pointed graph is like a Markov chain with weight 1 for each arrow.

If these arrows are weight by probabilities, then the above construction produces a [Markov chain](https://en.wikipedia.org/wiki/Markov_chain).

So the number of arrow or morphisms of a pointed graph is like a Markov chain with weight 1 for each arrow.