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Function to sum propagated (multiplied) edge weights between 2 nodes?

When companies partially own other companies in a web of connected ownership, the result is a WeightedAdjacencyMatrix A (in my case represented using SparseArray). To calculate how much of a "downstream" company j is owned by an "upstream" company i, I need to add (i,j) entry of the matrix A, as well as that of product A.A, and A.A.A, etc. Is there a more elegant way of summing up propagated (multiplied) edge weights between arbitrary pair of nodes in a weighted graph? Alternatively, is there a way to sum all orders of NeighborhoodGraph[i,o], over o = 1, ... ? Kind thanks!
Poomjai Nacaskul
ps. I think such calculations are often used in financial accounting to gauge relative degree of connectedness/influence/control between two entities.

POSTED BY: Poomjai Nacaskul
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