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Editorial Team
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Asked: 2026-06-03T09:10:54+00:00

I have an asymmetric directed graph with a set of probabilities (so the likelihood

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I have an asymmetric directed graph with a set of probabilities (so the likelihood that a person will move from point A to B, or point A to C, etc). Given a route through all the points, I would like to calculate the likelihood that each choice made in the route is a good choice.

As an example, suppose a graph of just 2 points.

//In a matrix, the probabilities might look like
//A     B
[ 0    0.9  //A
  0.1   0 ] //B

So the probability of moving from A to B is 0.9 and from B to A is 0.1. Given the route A->B, how correct is the first point (A), and how correct is the second point (B).

Suppose I have a bigger matrix with a route that goes A->B->C->D. So, some examples of what I would like to know:

  • How likely is it that A comes before B,C, & D
  • How likely is it that B comes after A
  • How likely is it that C & D come after B

Basically, at each point, I want to know the likelihood that the previous points come before the current and also the likelihood that the following points come after. I don’t need something that is statistically sound. Just an indicator that I can use for relative comparisons. Any ideas?

update: I see that this question is not useful to everyone but the answer is really useful to me so I’ve tried to make the description of the problem more clear and will include my answer shortly in case it helps someone.

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1 Answer

  1. Editorial Team

    After much thought, I came up with something that suits my needs. It still has the the same problem where to get an accurate answer would require checking every possible route. However, in my case, only checking direct and the first indirect routes are enough to give an idea of how “correct” my answer is.

    First I need the confidence for each probability. This is a separate calculation and is contained in a separate matrix (that maps 1 to 1 to the probability matrix). I just take the 1.0-confidenceInterval for each probability.

    If I have a route A->B->C->D, I calculate a “correctness indicator” for a point. It looks like I am getting some sort of average of a direct route and the first level of indirect routes.

    Some examples:

    Denote P(A,B) as probability that A comes before B
    Denote C(A,B) as confidence in the probability that A comes before B
    Denote P`(A,C) as confidence that A comes before C based on the indirect route A->B->C

    At point B, likelihood that A comes before it:

    indicator = P(A,B)*C(A,B)/C(A,B)

    At point C, likelihood that A & B come before:

    P(A,C) = P(A,B)*P(B,C)
    C    (A,C) = C(A,B)*C(B,C)

    indicator = [P(A,C)*C(A,C) + P(B,C)*C(B,C) + P'(A,C)*C'(A,C)]/[C(A,C)+C(B,C)+C'(A,C)]

    So this gives me some sort of indicator that is always between 0 and 1, and takes the first level indirect route into account (from->indirectPoint->to). It seems to provide the rough estimation I was looking for. It is not a great answer, but it does provide some estimate and since nothing else provides anything better, it is suitable

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