Double entry book keeping is just recording the "edge" in two places, once based on the source node, and once based on the target node. So you have a nice list of all edges coming from each node and a nice list of all edges going to each node. This was important before computers, since the process of looking up all edges going to/from a node would take real time and effort.

For your example of the landlord and the tenant, think, what if the landlord wanted a list of all payments that went into a specific bank account, what if the tenant wanted a list of all rent payments, etc. It's basically a database index to speed up those queries, but for a written database that is updates by hand. The fact that there is redundancy is just a bonus because you can now notice if the two places a piece of information are written down don't match.