DigraphAbsorptionProbabilities

[mtorpey]

This pull request adds the DigraphAbsorptionProbabilities attribute. Here's an explanation:

A random walk of infinite length through a digraph may pass through several different strongly connected components (SCCs). However, with probability 1 it must eventually reach an SCC which it can never leave, because the SCC has no out-edges leading to other SCCs. We may say that such an SCC has absorbed the random walk, and we can calculate the probability of each SCC absorbing a walk starting at a given vertex.

DigraphAbsorptionProbabilities returns an $m \times n$ matrix mat, where $m$ is the number of vertices in digraph and $n$ is the number of strongly connected components. Each entry mat[i][j] is a rational number representing the probability that an unbounded random walk starting at vertex i will be absorbed by strongly connected component j – that is, the probability that it will reach the component and never leave.

The algorithm is based on established theory for absorbing Markov chains. Once the strongly connected components are known, it pretty much comes down to one matrix multiplication.

This is the result of me looking into the game Soccer Dice, since I wanted to know the chance of a player scoring a goal starting from the black die. The answer is $\frac{1020}{4493}$, as shown in the test file!

[james-d-mitchell]

Looks great! Couple of minor comments, happy to merge after that!