In the drawing, are you sure A doesn't go back to cable #1? The wiring appears to be old romex with the exception of the newer romex that was tapped into the circuit.
Each cable should have a white and black wire.
By the number of wires connected to B I'd say it is a hot feed and C is a collection of neutrals.
Since there is a switch that affects this, A must be the switch feed or part of a switch leg. Take another close look inside the ceiling box and verify the wiring.