One way this could be calculated is to assign transition probabilities to the edges, and calculate the expected number of steps a random walk takes to reach the end. (wikipedia has the math required: https://en.wikipedia.org/wiki/Absorbing_Markov_chain#Expecte...)

I'm not sure how best to assign probabilities, or how sensitive it would be to that. Perhaps uniformly, or perhaps biased toward moving closer to the end state.