How can I compress a markov transition probability matrix?

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I'm performing a simple experiment. I have a markov transition matrix and I need to know how to compute a transition similarity matrix using spears algorithm. I'm following this paper(pages 8 and 9)

http://oro.open.ac.uk/2963/4/hong.pdf

I understand how to get the graph, the original probability matrix but I don't know how the original matrix gets converted to the transition similarity matrix.

Anyone can explain?

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