That explanation didn't click with me, either.

But I guess you could model each transaction as an edge, with the direction specifying which account is debited and which credited, and the weight determining the amount.

I don't find that particularly helpful myself, but I put that down to my unfamiliarity with graph data structures and the associated algorithms. Maybe there's something you can do more easily with a graph database, than you can if you have the same info in a table?