I don't understand how the current flows in the circuit below. How do I deal with the wire between nodes c and a, a and b, g and d. Why is the 5 Ω resistor shorted out? I am having a little trouble understanding what results from short circuiting.
Your convention is wrong. If you don't see any resistors across a line then you don't need to change the node name.
Here's the corrected circuit:
As you can see, both ends of the 5-Ohm resistor has "a", so it's shorted out.
There is no empty wires, just wires.
The convention in circuit drawing is that nodes connected by wires are at the same voltage, which means that the voltage at node a (Va) is the same as the voltage at node b (Vb) and c (Vc).
In turn, we know that the voltage across your 5 ohm resistor (Vc-Vb) = 0V, which means that it is in fact shorted out.