DebtRank: a PageRank-like measurement of systemic financial risk

I have a question for people smarter than me:

This method differs from PageRank by excluding walks along the graph that repeat edges. I always thought it was an interesting property that PageRank represents the probability of reaching a given page by following links at random. Does excluding cycles change this property? (My intuition is yes, but I'm bad at math!) If not, what would DebtRank values represent? Likelihood of some unit of debt ending up held by a particular institution?