Answer by periblepsis for Simplifying a circuit for nodal analysis

The following is your circuit:

^{simulate this circuit– Schematic created using CircuitLab}

Note that there are exactly three nodes.

So my question is this: is this a 3-node circuit or a 4-node circuitand if it is a 3-node circuit, what would be the simplified drawing?

The simplified drawing is as shown above and the circuit has three nodes (if you are a graph theorist). It has only two unknown node voltages, though.

You know that \$i_a=\frac{v_1}{R_2}\$ and therefore that \$i_2=3\cdot\frac{v_1}{R_2}\$.

Using Norton to Thévenin conversions you can then get:

^{simulate this circuit}

The above requires only the solution of a single equation to get \$v_1\$. And from there, the rest just falls out.

But the above goes above and beyond your question.